deep_causality_cfd 0.2.0

Counterfactual Computational fluid dynamics solvers and the Flow DSL.
Documentation 
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/*
 * SPDX-License-Identifier: MIT
 * Copyright (c) 2023 - 2026. The DeepCausality Authors and Contributors. All Rights Reserved.
 */

//! The `MetricProvider` seam (design D8): a static-dispatch trait that lets the compressible marcher run
//! generically over *any* structured coordinate, so geometry is **data**, not a code path.
//!
//! A marcher written over `M: MetricProvider<R>` consumes only "there is a computational lattice, a way
//! to sample a field onto it, a physical gradient, and a Jacobian volume factor". `CartesianIdentity` is
//! the capture limit (any geometry, high rank); [`BodyFittedCoordinate`](BodyFittedCoordinate) is
//! the fitted limit (this geometry, `O(10)` rank). Body-fittedness becomes a choice of impl, recovering
//! generality at zero asymptotic rank cost — the result the `qtt_blend_metric` study measured.
//!
//! The continuous body-fit blend parameter `λ` is supplied by
//! [`BlendedMap`](crate::coordinate::BlendedMap), which computes both charts' **forward** Jacobians
//! analytically and exposes the blended *inverse* metric through this trait. It carries a validity
//! precondition this trait cannot express: the blended map must stay invertible, i.e. `det J` one-signed
//! over the closed domain. `BlendedMap::new` scans for that and refuses a folding configuration, but a
//! hand-written `MetricProvider` impl is **not** checked, so a caller supplying its own must respect it.
//! The blend is validated numerically by `studies/qtt_blend_metric`.
//!
//! **Scope of the seam.** This trait carries the contravariant basis and the Jacobian volume factor, and
//! nothing else. That is enough for the first-order chain-rule gradient the compressible marchers use.
//! Second-order or genuinely covariant operators (a curvilinear Laplacian, covariant derivatives) need
//! the metric tensor `g` and the Christoffel symbols as well, which would extend this trait; a consumer
//! should not assume the present seam suffices for them.

use crate::CfdScalar;
use deep_causality_algebra::ConjugateScalar;
use deep_causality_physics::PhysicsError;
use deep_causality_tensor::CausalTensorTrain;

/// A structured curvilinear coordinate over a `2^Lx × 2^Ly` computational lattice, supplying the pieces a
/// compressible marcher needs: field sampling, the chain-rule physical gradient, and the Jacobian volume
/// factor — all carried as low-rank tensor trains. Static dispatch only (used as a generic bound).
pub trait MetricProvider<R>
where
    R: CfdScalar + ConjugateScalar<Real = R>,
{
    /// The computational lattice mode counts `(Lx, Ly)` (grid is `2^Lx × 2^Ly`).
    fn dims(&self) -> (usize, usize);

    /// Sample `f(ξ, η)` on the computational lattice (`ξ_i = i/Nx`, `η_j = j/Ny`) and QTT-encode it.
    ///
    /// # Errors
    /// Propagates sampling / codec errors.
    fn sample<F>(&self, f: F) -> Result<CausalTensorTrain<R>, PhysicsError>
    where
        F: Fn(R, R) -> R;

    /// The **physical** gradient `(∂u/∂x, ∂u/∂y)` of a field `u` carried in this coordinate, via the
    /// chain rule and the low-rank metric.
    ///
    /// # Errors
    /// Propagates apply / Hadamard / rounding errors.
    fn physical_gradient(
        &self,
        u: &CausalTensorTrain<R>,
    ) -> Result<(CausalTensorTrain<R>, CausalTensorTrain<R>), PhysicsError>;

    /// The Jacobian determinant `|J|` (the conservative volume factor) as a low-rank tensor train.
    fn jacobian(&self) -> &CausalTensorTrain<R>;
}