pyxfem.solidmechanics.finite_volume_2d_hyperelasticity module

Created on Thu Mar 7 11:17:17 2024 @author: nchevaug 2D Explicit Lagrangian Finite Volume Solver (GLACE Scheme).

Philosophy & Architecture: This module implements the Godunov-type Lagrangian Scheme for Compressible Euler equations (GLACE). It computes the evolution of a fluid on an unstructured 2D triangular mesh moving with the fluid velocity (Lagrangian framework).

The solver features a dual-execution architecture: 1. Pure NumPy (Fallback): Fully vectorized array operations. 2. Numba JIT (HPC Mode): Aggressively optimized loop-level parallelism

(prange), avoiding heap allocations and leveraging hardware registers for the nodal Riemann solver.

class pyxfem.solidmechanics.finite_volume_2d_hyperelasticity.Additional_MeshStruct(XY, tXY, F0, txy, iF0, F1, F)

Bases: NamedTuple

F: NDArray[float64]

Alias for field number 6

F0: NDArray[float64]

Alias for field number 2

F1: NDArray[float64]

Alias for field number 5

XY: NDArray[float64]

Alias for field number 0

iF0: NDArray[float64]

Alias for field number 4

tXY: NDArray[float64]

Alias for field number 1

txy: NDArray[float64]

Alias for field number 3

class pyxfem.solidmechanics.finite_volume_2d_hyperelasticity.ConservationLawManager_Hyperelasticity(hyplaw, nbdata)

Bases: ConservativeLawManager

acoustic_impedance_tensor(n, outZ=None)

Compute the impedance

conservative_to_primal(cell_measure)

Compute from U (the conservative variable) the primal Variable W depending on the law

static conservative_to_primal_(m, mu, mF, cell_measure, fun_sigma_c, props_sigma_c, rho, u, sigma, c)

pyxfem.solidmechanics.finite_volume_2d_hyperelasticity.GELEES_bc_set_external_pressure(vids: NDArray[int64], ps: NDArray[float64], mesh: GELEES_MeshStruct, out_vA: NDArray[float64], out_vb: NDArray[float64]) → None

Applies external pressure directly to the RHS vectors $b_{jr}$ of boundary nodes.

pyxfem.solidmechanics.finite_volume_2d_hyperelasticity.GELEES_bc_set_sliding_wall(vids: NDArray[int64], NxN: NDArray[float64], ImNxN: NDArray[float64], vA: NDArray[float64], vb: NDArray[float64]) → None

Applies a sliding wall (slip) boundary condition to the global nodal linear system.

This function modifies the assembled $A_r$ matrices and $b_r$ vectors in-place for the nodes located on a sliding wall. It ensures that the velocity vector resulting from the linear system solver will have zero component normal to the wall ($u cdot n = 0$).

The algebraic modification projects the system onto the tangent plane: $A_{new} = (I - n otimes n) A_r (I - n otimes n) + mathrm{Tr}(A_r)(n otimes n)$ $b_{new} = (I - n otimes n) b_r$

Adding the trace back to the normal component ensures the modified matrix remains strictly invertible and well-conditioned.

Parameters:

• vids (npt.NDArray[np.uint64]) – 1D array of length (n_boundary_nodes). The global indices of the vertices located on the sliding wall.

• NxN (FloatArray) – 3D array of shape (n_boundary_nodes, 2, 2). The dyadic tensor product of the normal vectors ($n otimes n$) at each boundary node.

• ImNxN (FloatArray) – 3D array of shape (n_boundary_nodes, 2, 2). The tangent projection matrix ($I - n otimes n$) at each boundary node.

• vA (FloatArray) – 3D array of shape (nverts, 2, 2). The global assembled $A_r$ matrices for all nodes in the mesh. Modified in-place.

• vb (FloatArray) – 2D array of shape (nverts, 2). The global assembled $b_r$ vectors for all nodes in the mesh. Modified in-place.

Returns:

The global vA and vb arrays are modified in-place to reflect the boundary constraints.

Return type:

None

class pyxfem.solidmechanics.finite_volume_2d_hyperelasticity.GlaceExplicitLagrangian_HyperElasticty_EquationSolver(law: HyperElasticMaterial, XY: NDArray[float64], xy: NDArray[float64], tris: NDArray[int64], boundary_conditions: Dict[str, Any], use_numba: bool = False)

Bases: GlaceExplicitLagrangianBaseSolver

A 2D Explicit Lagrangian Finite Volume Solver for the Euler Equations using the GLACE (Godunov-type Lagrangian Scheme for Compressible Euler) scheme.

This class manages the mesh topology, physical state variables, boundary conditions, and time integration (both in pure NumPy and Numba JIT modes).

static cell_soundspeed(cvZ, cc)

static cell_soundspeed_pnjit(cvZ, cc)

compute_impedance_tensors(mesh: GELEES_MeshStruct, out_cvZ: NDArray[float64] | None = None)

Compute the impdence tensor Z, per cell vertex (cv)

critical_timestep() → float

Computes the maximum allowable critical time step for the entire mesh based on the CFL condition (acoustic wave speeds).

Returns:

dtmax – The critical time step (dt).

Return type:

float

set_initial_state(velocity: Callable[[NDArray[float64]], NDArray[float64]]) → None

Sets the initial macroscopic state of the fluid for all cells.

Parameters:

• density (Callable[[FloatArray], FloatArray]) – A function taking cell center coordinates (N, 2) and returning an array of initial densities (N,).

• velocity (Callable[[FloatArray], FloatArray]) – A function taking cell center coordinates (N, 2) and returning an array of initial velocity vectors (N, 2).

• pressure (Callable[[FloatArray], FloatArray]) – A function taking cell center coordinates (N, 2) and returning an array of initial pressures (N,).

step(dt: float) → float

Advances the simulation by one time step dt using the pure NumPy solver.

Parameters:

dt (float) – The duration of the time step.

Returns:

dtcnew – The new computed critical time step for the next iteration.

Return type:

float

step_np(dt: float) → float

Advances the simulation by one time step dt using the pure NumPy solver.

Parameters:

dt (float) – The duration of the time step.

Returns:

dtcnew – The new computed critical time step for the next iteration.

Return type:

float

pyxfem.solidmechanics.finite_volume_2d_hyperelasticity.setup_AdditionalMeshStruct(XY, xy, tris)

pyxfem.solidmechanics.finite_volume_2d_hyperelasticity.update_AdditionalMeshStruct(mesh: GELEES_MeshStruct, additional_mesh_data: Additional_MeshStruct)

pyxfem.solidmechanics.finite_volume_2d_hyperelasticity.update_AdditionalMeshStruct_pnjit(mesh: GELEES_MeshStruct, additional_mesh_data: Additional_MeshStruct)

pyxfem.solidmechanics.finite_volume_2d_hyperelasticity.update_conservative_vars_kernel(cvqflux, cvu, dt, in_out_U_cell)

pyxfem.solidmechanics.finite_volume_2d_hyperelasticity.update_conservative_vars_pnjit(cvqflux, cvu, dt, in_out_U)