deep_causality_physics 0.6.1

/*
 * SPDX-License-Identifier: MIT
 * Copyright (c) 2023 - 2026. The DeepCausality Authors and Contributors. All Rights Reserved.
 */

use crate::kernels::fluids::{
    boundary_layer, coherent_structures, compressible, constitutive, dimensionless, governing,
    ideal_flow, kinematics, mechanics, turbulence,
};
use crate::theories::fluid_dynamics::{compressible_ns, euler, incompressible_ns, stokes};
use crate::{
    AccelerationVector, Density, KinematicViscosity, Length, Pressure, ReynoldsStress,
    RotationRateTensor, SpecificEnthalpy, Speed, StrainRateTensor, Temperature, Velocity3,
    VelocityGradient, Viscosity, ViscousStress, VorticityVector, WallShearStress,
};
use core::fmt::Debug;
use deep_causality_core::{CausalityError, PropagatingEffect};
use deep_causality_num::{FromPrimitive, RealField};

/// Causal wrapper for [`mechanics::hydrostatic_pressure_kernel`].
pub fn hydrostatic_pressure<R>(
    p0: &Pressure<R>,
    density: &Density<R>,
    depth: &Length<R>,
) -> PropagatingEffect<Pressure<R>>
where
    R: RealField + FromPrimitive + Debug,
{
    match mechanics::hydrostatic_pressure_kernel(p0, density, depth) {
        Ok(p) => PropagatingEffect::pure(p),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`mechanics::bernoulli_pressure_kernel`].
pub fn bernoulli_pressure<R>(
    p1: &Pressure<R>,
    v1: &Speed<R>,
    h1: &Length<R>,
    v2: &Speed<R>,
    h2: &Length<R>,
    density: &Density<R>,
) -> PropagatingEffect<Pressure<R>>
where
    R: RealField + FromPrimitive + Debug,
{
    match mechanics::bernoulli_pressure_kernel(p1, v1, h1, v2, h2, density) {
        Ok(p) => PropagatingEffect::pure(p),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

// =============================================================================
// Kinematic kernel wrappers
// =============================================================================

/// Causal wrapper for [`kinematics::strain_rate_tensor_kernel`].
pub fn strain_rate_tensor<R>(grad_u: &VelocityGradient<R>) -> PropagatingEffect<StrainRateTensor<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match kinematics::strain_rate_tensor_kernel(grad_u) {
        Ok(s) => PropagatingEffect::pure(s),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`kinematics::rotation_rate_tensor_kernel`].
pub fn rotation_rate_tensor<R>(
    grad_u: &VelocityGradient<R>,
) -> PropagatingEffect<RotationRateTensor<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match kinematics::rotation_rate_tensor_kernel(grad_u) {
        Ok(o) => PropagatingEffect::pure(o),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`kinematics::vorticity_from_gradient_kernel`].
pub fn vorticity_from_gradient<R>(
    grad_u: &VelocityGradient<R>,
) -> PropagatingEffect<VorticityVector<R>>
where
    R: RealField + Debug + 'static,
{
    PropagatingEffect::pure(kinematics::vorticity_from_gradient_kernel(grad_u))
}

/// Causal wrapper for [`kinematics::velocity_gradient_invariants_kernel`].
pub fn velocity_gradient_invariants<R>(grad_u: &VelocityGradient<R>) -> PropagatingEffect<(R, R, R)>
where
    R: RealField + FromPrimitive + Debug + Default + 'static,
{
    match kinematics::velocity_gradient_invariants_kernel(grad_u) {
        Ok(inv) => PropagatingEffect::pure(inv),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`kinematics::helicity_density_kernel`].
pub fn helicity_density<R>(u: &Velocity3<R>, omega: &VorticityVector<R>) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    PropagatingEffect::pure(kinematics::helicity_density_kernel(u, omega))
}

/// Causal wrapper for [`kinematics::enstrophy_density_kernel`].
pub fn enstrophy_density<R>(omega: &VorticityVector<R>) -> PropagatingEffect<R>
where
    R: RealField + FromPrimitive + Debug + Default + 'static,
{
    match kinematics::enstrophy_density_kernel(omega) {
        Ok(e) => PropagatingEffect::pure(e),
        Err(err) => PropagatingEffect::from_error(CausalityError::from(err)),
    }
}

// =============================================================================
// Governing-equation kernel wrappers
// =============================================================================

/// Causal wrapper for [`governing::convective_acceleration_kernel`].
pub fn convective_acceleration<R>(
    u: &Velocity3<R>,
    grad_u: &VelocityGradient<R>,
) -> PropagatingEffect<AccelerationVector<R>>
where
    R: RealField + Debug + 'static,
{
    PropagatingEffect::pure(governing::convective_acceleration_kernel(u, grad_u))
}

/// Causal wrapper for [`governing::viscous_diffusion_kernel`].
pub fn viscous_diffusion<R>(
    nu: &KinematicViscosity<R>,
    laplacian_u: &[R; 3],
) -> PropagatingEffect<AccelerationVector<R>>
where
    R: RealField + Debug + 'static,
{
    PropagatingEffect::pure(governing::viscous_diffusion_kernel(nu, laplacian_u))
}

/// Causal wrapper for [`governing::pressure_gradient_force_kernel`].
pub fn pressure_gradient_force<R>(
    rho: &Density<R>,
    grad_p: &[R; 3],
) -> PropagatingEffect<AccelerationVector<R>>
where
    R: RealField + Debug + 'static,
{
    match governing::pressure_gradient_force_kernel(rho, grad_p) {
        Ok(a) => PropagatingEffect::pure(a),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`governing::continuity_rhs_kernel`].
pub fn continuity_rhs<R>(
    rho: &Density<R>,
    u: &Velocity3<R>,
    grad_rho: &[R; 3],
    div_u: R,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    PropagatingEffect::pure(governing::continuity_rhs_kernel(rho, u, grad_rho, div_u))
}

/// Causal wrapper for [`governing::vorticity_transport_kernel`].
pub fn vorticity_transport<R>(
    omega: &VorticityVector<R>,
    u: &Velocity3<R>,
    grad_u: &VelocityGradient<R>,
    grad_omega: &[[R; 3]; 3],
    laplacian_omega: &[R; 3],
    nu: &KinematicViscosity<R>,
) -> PropagatingEffect<AccelerationVector<R>>
where
    R: RealField + Debug + 'static,
{
    PropagatingEffect::pure(governing::vorticity_transport_kernel(
        omega,
        u,
        grad_u,
        grad_omega,
        laplacian_omega,
        nu,
    ))
}

/// Causal wrapper for [`governing::scalar_advection_diffusion_kernel`].
pub fn scalar_advection_diffusion<R>(
    u: &Velocity3<R>,
    grad_phi: &[R; 3],
    laplacian_phi: R,
    diffusivity: R,
    source: R,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    PropagatingEffect::pure(governing::scalar_advection_diffusion_kernel(
        u,
        grad_phi,
        laplacian_phi,
        diffusivity,
        source,
    ))
}

/// Causal wrapper for [`governing::kinetic_energy_density_kernel`].
pub fn kinetic_energy_density<R>(rho: &Density<R>, u: &Velocity3<R>) -> PropagatingEffect<R>
where
    R: RealField + FromPrimitive + Debug + Default + 'static,
{
    match governing::kinetic_energy_density_kernel(rho, u) {
        Ok(e) => PropagatingEffect::pure(e),
        Err(err) => PropagatingEffect::from_error(CausalityError::from(err)),
    }
}

/// Causal wrapper for [`governing::viscous_dissipation_rate_kernel`].
pub fn viscous_dissipation_rate<R>(
    tau: &ViscousStress<R>,
    grad_u: &VelocityGradient<R>,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    PropagatingEffect::pure(governing::viscous_dissipation_rate_kernel(tau, grad_u))
}

/// Causal wrapper for [`governing::pressure_work_kernel`].
pub fn pressure_work<R>(p: &Pressure<R>, div_u: R) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    PropagatingEffect::pure(governing::pressure_work_kernel(p, div_u))
}

// =============================================================================
// Constitutive kernel wrappers
// =============================================================================

/// Causal wrapper for [`constitutive::newtonian_viscous_stress_kernel`].
pub fn newtonian_viscous_stress<R>(
    mu: &Viscosity<R>,
    strain_rate: &StrainRateTensor<R>,
    div_u: R,
) -> PropagatingEffect<ViscousStress<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match constitutive::newtonian_viscous_stress_kernel(mu, strain_rate, div_u) {
        Ok(tau) => PropagatingEffect::pure(tau),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`constitutive::newtonian_viscous_stress_with_bulk_kernel`].
pub fn newtonian_viscous_stress_with_bulk<R>(
    mu: &Viscosity<R>,
    zeta: &Viscosity<R>,
    strain_rate: &StrainRateTensor<R>,
    div_u: R,
) -> PropagatingEffect<ViscousStress<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match constitutive::newtonian_viscous_stress_with_bulk_kernel(mu, zeta, strain_rate, div_u) {
        Ok(tau) => PropagatingEffect::pure(tau),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`constitutive::power_law_apparent_viscosity_kernel`].
pub fn power_law_apparent_viscosity<R>(
    consistency: R,
    flow_index: R,
    shear_rate: R,
) -> PropagatingEffect<Viscosity<R>>
where
    R: RealField + Debug + 'static,
{
    match constitutive::power_law_apparent_viscosity_kernel(consistency, flow_index, shear_rate) {
        Ok(mu) => PropagatingEffect::pure(mu),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

// =============================================================================
// Dimensionless number wrappers — each lifts the kernel's `Result<R, _>` into
// a `PropagatingEffect<R>` via `pure` / `from_error`.
// =============================================================================

/// Causal wrapper for [`dimensionless::reynolds_number_kernel`].
pub fn reynolds_number<R>(
    u: &Speed<R>,
    length: &Length<R>,
    nu: &KinematicViscosity<R>,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::reynolds_number_kernel(u, length, nu) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::mach_number_kernel`].
pub fn mach_number<R>(u: &Speed<R>, sound_speed: &Speed<R>) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::mach_number_kernel(u, sound_speed) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::froude_number_kernel`].
pub fn froude_number<R>(u: &Speed<R>, gravity: R, length: &Length<R>) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::froude_number_kernel(u, gravity, length) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::weber_number_kernel`].
pub fn weber_number<R>(
    rho: &Density<R>,
    u: &Speed<R>,
    length: &Length<R>,
    surface_tension: R,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::weber_number_kernel(rho, u, length, surface_tension) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::prandtl_number_kernel`].
pub fn prandtl_number<R>(nu: &KinematicViscosity<R>, thermal_diffusivity: R) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::prandtl_number_kernel(nu, thermal_diffusivity) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::peclet_number_kernel`].
pub fn peclet_number<R>(
    u: &Speed<R>,
    length: &Length<R>,
    thermal_diffusivity: R,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::peclet_number_kernel(u, length, thermal_diffusivity) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::strouhal_number_kernel`].
pub fn strouhal_number<R>(frequency: R, length: &Length<R>, u: &Speed<R>) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::strouhal_number_kernel(frequency, length, u) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::knudsen_number_kernel`].
pub fn knudsen_number<R>(mean_free_path: R, length: &Length<R>) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::knudsen_number_kernel(mean_free_path, length) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::richardson_number_kernel`].
pub fn richardson_number<R>(
    gravity: R,
    expansion_coefficient: R,
    delta_temperature: R,
    length: &Length<R>,
    u: &Speed<R>,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::richardson_number_kernel(
        gravity,
        expansion_coefficient,
        delta_temperature,
        length,
        u,
    ) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::rayleigh_number_kernel`].
pub fn rayleigh_number<R>(
    gravity: R,
    expansion_coefficient: R,
    delta_temperature: R,
    length: &Length<R>,
    nu: &KinematicViscosity<R>,
    thermal_diffusivity: R,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::rayleigh_number_kernel(
        gravity,
        expansion_coefficient,
        delta_temperature,
        length,
        nu,
        thermal_diffusivity,
    ) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::grashof_number_kernel`].
pub fn grashof_number<R>(
    gravity: R,
    expansion_coefficient: R,
    delta_temperature: R,
    length: &Length<R>,
    nu: &KinematicViscosity<R>,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::grashof_number_kernel(
        gravity,
        expansion_coefficient,
        delta_temperature,
        length,
        nu,
    ) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::eckert_number_kernel`].
pub fn eckert_number<R>(
    u: &Speed<R>,
    specific_heat: R,
    delta_temperature: R,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::eckert_number_kernel(u, specific_heat, delta_temperature) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::schmidt_number_kernel`].
pub fn schmidt_number<R>(nu: &KinematicViscosity<R>, mass_diffusivity: R) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::schmidt_number_kernel(nu, mass_diffusivity) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::lewis_number_kernel`].
pub fn lewis_number<R>(thermal_diffusivity: R, mass_diffusivity: R) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::lewis_number_kernel(thermal_diffusivity, mass_diffusivity) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::particle_stokes_number_kernel`].
pub fn particle_stokes_number<R>(
    particle_relaxation_time: R,
    u: &Speed<R>,
    length: &Length<R>,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::particle_stokes_number_kernel(particle_relaxation_time, u, length) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::capillary_number_kernel`].
pub fn capillary_number<R>(
    mu: &Viscosity<R>,
    u: &Speed<R>,
    surface_tension: R,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::capillary_number_kernel(mu, u, surface_tension) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::bond_number_kernel`].
pub fn bond_number<R>(
    rho: &Density<R>,
    gravity: R,
    length: &Length<R>,
    surface_tension: R,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::bond_number_kernel(rho, gravity, length, surface_tension) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`dimensionless::nusselt_number_kernel`].
pub fn nusselt_number<R>(
    heat_transfer_coefficient: R,
    length: &Length<R>,
    thermal_conductivity: R,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match dimensionless::nusselt_number_kernel(
        heat_transfer_coefficient,
        length,
        thermal_conductivity,
    ) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

// =============================================================================
// Turbulence wrappers
// =============================================================================

/// Causal wrapper for [`turbulence::turbulent_kinetic_energy_kernel`].
pub fn turbulent_kinetic_energy<R>(u_prime: &Velocity3<R>) -> PropagatingEffect<R>
where
    R: RealField + FromPrimitive + Debug + Default + 'static,
{
    match turbulence::turbulent_kinetic_energy_kernel(u_prime) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`turbulence::dissipation_rate_kernel`].
pub fn dissipation_rate<R>(
    nu: &KinematicViscosity<R>,
    grad_u_prime: &VelocityGradient<R>,
) -> PropagatingEffect<R>
where
    R: RealField + FromPrimitive + Debug + Default + 'static,
{
    match turbulence::dissipation_rate_kernel(nu, grad_u_prime) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`turbulence::kolmogorov_length_kernel`].
pub fn kolmogorov_length<R>(nu: &KinematicViscosity<R>, epsilon: R) -> PropagatingEffect<Length<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match turbulence::kolmogorov_length_kernel(nu, epsilon) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`turbulence::kolmogorov_time_kernel`].
pub fn kolmogorov_time<R>(nu: &KinematicViscosity<R>, epsilon: R) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match turbulence::kolmogorov_time_kernel(nu, epsilon) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`turbulence::kolmogorov_velocity_kernel`].
pub fn kolmogorov_velocity<R>(nu: &KinematicViscosity<R>, epsilon: R) -> PropagatingEffect<Speed<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match turbulence::kolmogorov_velocity_kernel(nu, epsilon) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`turbulence::taylor_microscale_kernel`].
pub fn taylor_microscale<R>(
    k_energy: R,
    epsilon: R,
    nu: &KinematicViscosity<R>,
) -> PropagatingEffect<Length<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match turbulence::taylor_microscale_kernel(k_energy, epsilon, nu) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`turbulence::integral_length_scale_kernel`].
pub fn integral_length_scale<R>(k_energy: R, epsilon: R) -> PropagatingEffect<Length<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match turbulence::integral_length_scale_kernel(k_energy, epsilon) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`turbulence::reynolds_stress_kernel`].
pub fn reynolds_stress<R>(
    u_prime_outer_u_prime: &StrainRateTensor<R>,
) -> PropagatingEffect<ReynoldsStress<R>>
where
    R: RealField + Debug + 'static,
{
    PropagatingEffect::pure(turbulence::reynolds_stress_kernel(u_prime_outer_u_prime))
}

/// Causal wrapper for [`turbulence::eddy_viscosity_boussinesq_kernel`].
pub fn eddy_viscosity_boussinesq<R>(
    reynolds_stress: &ReynoldsStress<R>,
    strain_rate_mean: &StrainRateTensor<R>,
    k_energy: R,
) -> PropagatingEffect<Viscosity<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match turbulence::eddy_viscosity_boussinesq_kernel(reynolds_stress, strain_rate_mean, k_energy)
    {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

// =============================================================================
// Coherent-structure detector wrappers
// =============================================================================

/// Causal wrapper for [`coherent_structures::q_criterion_kernel`].
pub fn q_criterion<R>(grad_u: &VelocityGradient<R>) -> PropagatingEffect<R>
where
    R: RealField + FromPrimitive + Debug + Default + 'static,
{
    match coherent_structures::q_criterion_kernel(grad_u) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`coherent_structures::delta_criterion_kernel`].
pub fn delta_criterion<R>(grad_u: &VelocityGradient<R>) -> PropagatingEffect<R>
where
    R: RealField + FromPrimitive + Debug + Default + 'static,
{
    match coherent_structures::delta_criterion_kernel(grad_u) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`coherent_structures::lambda2_kernel`].
pub fn lambda2<R>(grad_u: &VelocityGradient<R>) -> PropagatingEffect<R>
where
    R: RealField + FromPrimitive + Debug + Default + 'static,
{
    match coherent_structures::lambda2_kernel(grad_u) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`coherent_structures::swirling_strength_kernel`].
pub fn swirling_strength<R>(grad_u: &VelocityGradient<R>) -> PropagatingEffect<R>
where
    R: RealField + FromPrimitive + Debug + Default + 'static,
{
    match coherent_structures::swirling_strength_kernel(grad_u) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

// =============================================================================
// Compressible-flow thermodynamic wrappers
// =============================================================================

/// Causal wrapper for [`compressible::speed_of_sound_ideal_gas_kernel`].
pub fn speed_of_sound_ideal_gas<R>(
    gamma: R,
    r_specific: R,
    temperature: &Temperature<R>,
) -> PropagatingEffect<Speed<R>>
where
    R: RealField + Debug + 'static,
{
    match compressible::speed_of_sound_ideal_gas_kernel(gamma, r_specific, temperature) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`compressible::specific_enthalpy_kernel`].
pub fn specific_enthalpy<R>(
    cp: R,
    temperature: &Temperature<R>,
) -> PropagatingEffect<SpecificEnthalpy<R>>
where
    R: RealField + Debug + 'static,
{
    PropagatingEffect::pure(compressible::specific_enthalpy_kernel(cp, temperature))
}

/// Causal wrapper for [`compressible::total_enthalpy_kernel`].
pub fn total_enthalpy<R>(
    h: &SpecificEnthalpy<R>,
    u: &Velocity3<R>,
) -> PropagatingEffect<SpecificEnthalpy<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match compressible::total_enthalpy_kernel(h, u) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`compressible::total_pressure_isentropic_kernel`].
pub fn total_pressure_isentropic<R>(
    p: &Pressure<R>,
    mach: R,
    gamma: R,
) -> PropagatingEffect<Pressure<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match compressible::total_pressure_isentropic_kernel(p, mach, gamma) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`compressible::total_temperature_isentropic_kernel`].
pub fn total_temperature_isentropic<R>(
    t: &Temperature<R>,
    mach: R,
    gamma: R,
) -> PropagatingEffect<Temperature<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match compressible::total_temperature_isentropic_kernel(t, mach, gamma) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`compressible::entropy_production_rate_kernel`].
pub fn entropy_production_rate<R>(
    temperature: &Temperature<R>,
    tau: &ViscousStress<R>,
    grad_u: &VelocityGradient<R>,
    thermal_conductivity: R,
    grad_temperature: &[R; 3],
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match compressible::entropy_production_rate_kernel(
        temperature,
        tau,
        grad_u,
        thermal_conductivity,
        grad_temperature,
    ) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

// =============================================================================
// Boundary-layer wrappers
// =============================================================================

/// Causal wrapper for [`boundary_layer::wall_shear_stress_newtonian_kernel`].
pub fn wall_shear_stress_newtonian<R>(
    mu: &Viscosity<R>,
    du_dy_wall: R,
) -> PropagatingEffect<WallShearStress<R>>
where
    R: RealField + Debug + 'static,
{
    match boundary_layer::wall_shear_stress_newtonian_kernel(mu, du_dy_wall) {
        Ok(t) => PropagatingEffect::pure(t),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`boundary_layer::friction_velocity_kernel`].
pub fn friction_velocity<R>(
    tau_w: &WallShearStress<R>,
    rho: &Density<R>,
) -> PropagatingEffect<Speed<R>>
where
    R: RealField + Debug + 'static,
{
    match boundary_layer::friction_velocity_kernel(tau_w, rho) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`boundary_layer::viscous_length_scale_kernel`].
pub fn viscous_length_scale<R>(
    nu: &KinematicViscosity<R>,
    u_tau: &Speed<R>,
) -> PropagatingEffect<Length<R>>
where
    R: RealField + Debug + 'static,
{
    match boundary_layer::viscous_length_scale_kernel(nu, u_tau) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`boundary_layer::y_plus_kernel`].
pub fn y_plus<R>(
    y: &Length<R>,
    u_tau: &Speed<R>,
    nu: &KinematicViscosity<R>,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match boundary_layer::y_plus_kernel(y, u_tau, nu) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`boundary_layer::viscous_sublayer_velocity_kernel`].
pub fn viscous_sublayer_velocity<R>(y_plus: R) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    PropagatingEffect::pure(boundary_layer::viscous_sublayer_velocity_kernel(y_plus))
}

/// Causal wrapper for [`boundary_layer::log_law_velocity_kernel`].
pub fn log_law_velocity<R>(y_plus: R, kappa: R, b: R) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match boundary_layer::log_law_velocity_kernel(y_plus, kappa, b) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`boundary_layer::skin_friction_coefficient_kernel`].
pub fn skin_friction_coefficient<R>(
    tau_w: &WallShearStress<R>,
    rho: &Density<R>,
    u_inf: &Speed<R>,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match boundary_layer::skin_friction_coefficient_kernel(tau_w, rho, u_inf) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

// =============================================================================
// Ideal-flow primitive wrappers
// =============================================================================

/// Causal wrapper for [`ideal_flow::dynamic_pressure_kernel`].
pub fn dynamic_pressure<R>(rho: &Density<R>, u: &Speed<R>) -> PropagatingEffect<Pressure<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match ideal_flow::dynamic_pressure_kernel(rho, u) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`ideal_flow::bernoulli_total_head_kernel`].
pub fn bernoulli_total_head<R>(
    p: &Pressure<R>,
    rho: &Density<R>,
    u: &Speed<R>,
    h: &Length<R>,
) -> PropagatingEffect<Length<R>>
where
    R: RealField + FromPrimitive + Debug + 'static,
{
    match ideal_flow::bernoulli_total_head_kernel(p, rho, u, h) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`ideal_flow::stream_function_2d_kernel`].
pub fn stream_function_2d<R>(u: R, v: R, dx: R, dy: R) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    PropagatingEffect::pure(ideal_flow::stream_function_2d_kernel(u, v, dx, dy))
}

/// Causal wrapper for [`ideal_flow::velocity_potential_2d_kernel`].
pub fn velocity_potential_2d<R>(u: R, v: R, dx: R, dy: R) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    PropagatingEffect::pure(ideal_flow::velocity_potential_2d_kernel(u, v, dx, dy))
}

/// Causal wrapper for [`ideal_flow::circulation_kernel`].
pub fn circulation<R>(
    velocity_at_loop_points: &[Velocity3<R>],
    tangents: &[[R; 3]],
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    match ideal_flow::circulation_kernel(velocity_at_loop_points, tangents) {
        Ok(v) => PropagatingEffect::pure(v),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`ideal_flow::kutta_joukowski_lift_kernel`].
pub fn kutta_joukowski_lift<R>(
    rho: &Density<R>,
    u_inf: &Speed<R>,
    circulation: R,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    PropagatingEffect::pure(ideal_flow::kutta_joukowski_lift_kernel(
        rho,
        u_inf,
        circulation,
    ))
}

// =============================================================================
// Theory layer — incompressible Newtonian NS regime
// =============================================================================

/// Causal wrapper for [`incompressible_ns::incompressible_ns_rhs_kernel`].
pub fn incompressible_ns_rhs<R>(
    u: &Velocity3<R>,
    grad_u: &VelocityGradient<R>,
    laplacian_u: &[R; 3],
    grad_p: &[R; 3],
    rho: &Density<R>,
    nu: &KinematicViscosity<R>,
    body_force_per_mass: &AccelerationVector<R>,
) -> PropagatingEffect<AccelerationVector<R>>
where
    R: RealField + Debug + 'static,
{
    match incompressible_ns::incompressible_ns_rhs_kernel(
        u,
        grad_u,
        laplacian_u,
        grad_p,
        rho,
        nu,
        body_force_per_mass,
    ) {
        Ok(a) => PropagatingEffect::pure(a),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

// =============================================================================
// Theory layer — Euler regime (inviscid)
// =============================================================================

/// Causal wrapper for [`euler::euler_momentum_rhs_kernel`].
pub fn euler_momentum_rhs<R>(
    u: &Velocity3<R>,
    grad_u: &VelocityGradient<R>,
    grad_p: &[R; 3],
    rho: &Density<R>,
    body_force_per_mass: &AccelerationVector<R>,
) -> PropagatingEffect<AccelerationVector<R>>
where
    R: RealField + Debug + 'static,
{
    match euler::euler_momentum_rhs_kernel(u, grad_u, grad_p, rho, body_force_per_mass) {
        Ok(a) => PropagatingEffect::pure(a),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

// =============================================================================
// Theory layer — Stokes regime (creeping flow)
// =============================================================================

/// Causal wrapper for [`stokes::stokes_momentum_rhs_kernel`].
pub fn stokes_momentum_rhs<R>(
    laplacian_u: &[R; 3],
    grad_p: &[R; 3],
    rho: &Density<R>,
    nu: &KinematicViscosity<R>,
    body_force_per_mass: &AccelerationVector<R>,
) -> PropagatingEffect<AccelerationVector<R>>
where
    R: RealField + Debug + 'static,
{
    match stokes::stokes_momentum_rhs_kernel(laplacian_u, grad_p, rho, nu, body_force_per_mass) {
        Ok(a) => PropagatingEffect::pure(a),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

// =============================================================================
// Theory layer — compressible Newtonian NS regime
// =============================================================================

/// Causal wrapper for [`compressible_ns::compressible_ns_continuity_rhs_kernel`].
pub fn compressible_ns_continuity_rhs<R>(
    rho: &Density<R>,
    u: &Velocity3<R>,
    grad_rho: &[R; 3],
    div_u: R,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    PropagatingEffect::pure(compressible_ns::compressible_ns_continuity_rhs_kernel(
        rho, u, grad_rho, div_u,
    ))
}

/// Causal wrapper for [`compressible_ns::compressible_ns_momentum_rhs_kernel`].
pub fn compressible_ns_momentum_rhs<R>(
    u: &Velocity3<R>,
    grad_u: &VelocityGradient<R>,
    grad_p: &[R; 3],
    div_tau: &[R; 3],
    rho: &Density<R>,
    body_force_per_mass: &AccelerationVector<R>,
) -> PropagatingEffect<AccelerationVector<R>>
where
    R: RealField + Debug + 'static,
{
    match compressible_ns::compressible_ns_momentum_rhs_kernel(
        u,
        grad_u,
        grad_p,
        div_tau,
        rho,
        body_force_per_mass,
    ) {
        Ok(a) => PropagatingEffect::pure(a),
        Err(e) => PropagatingEffect::from_error(CausalityError::from(e)),
    }
}

/// Causal wrapper for [`compressible_ns::compressible_ns_energy_rhs_kernel`].
pub fn compressible_ns_energy_rhs<R>(
    rho: &Density<R>,
    u: &Velocity3<R>,
    div_rho_u_e: R,
    div_p_u: R,
    div_tau_dot_u: R,
    div_q: R,
    body_force_per_mass: &AccelerationVector<R>,
) -> PropagatingEffect<R>
where
    R: RealField + Debug + Default + 'static,
{
    PropagatingEffect::pure(compressible_ns::compressible_ns_energy_rhs_kernel(
        rho,
        u,
        div_rho_u_e,
        div_p_u,
        div_tau_dot_u,
        div_q,
        body_force_per_mass,
    ))
}