Solver

SPH Solver

Weakly compressible SPH solver.

jax_sph.solver.rho_evol_fn(rho, mass, u, grad_w_dist, i_s, j_s, dt, N, **kwargs)

Density evolution according to Adami et al. 2013.

jax_sph.solver.rho_evol_riemann_fn_wrapper(kernel_fn, eos, c_ref)

Density evolution according to Zhang et al. 2017.

jax_sph.solver.rho_renorm_fn(rho, mass, i_s, j_s, w_dist, N)

Renormalization of density according to Zhang et al. 2017.

jax_sph.solver.rho_summation_fn(mass, i_s, w_dist, N)

Density summation.

jax_sph.solver.wall_phi_vec_wrapper(kernel_fn)

Compute the wall phi vector according to Zhang et al. 2017.

jax_sph.solver.acceleration_tvf_fn_wrapper(kernel_fn)

Transport velocity formulation acceleration according to Adami et al. 2013.

jax_sph.solver.tvf_stress_fn(rho: float, u, v)

Transport velocity stress tensor. See ‘A’ under (Eq. 4) in Adami et al. 2013.

jax_sph.solver.acceleration_standard_fn_wrapper(kernel_fn)

Standard SPH acceleration according to Adami et al. 2012.

jax_sph.solver.acceleration_riemann_fn_wrapper(kernel_fn, eos, beta_fn, eta_limiter)

Riemann solver acceleration according to Zhang et al. 2017.

jax_sph.solver.artificial_viscosity_fn_wrapper(dx, artificial_alpha, u_ref=1.0)

Artificial viscosity according to Adami et al. 2012.

jax_sph.solver.gwbc_fn_wrapper(is_free_slip, is_heat_conduction, eos)

Enforce wall boundary conditions by treating boundary particles in a special way.

If solid walls -> apply BC tricks

Update dummy particles before acceleration computation (if appl.).

Steps for boundary particles:

• sum pressure over fluid with sheparding

• inverse EoS for density

• sum velocity over fluid with sheparding and * (-1)

• if free-slip: project velocity onto normal vector

• subtract that from 2 * u_wall - keeps lid intact

Based on: “A generalized wall boundary condition for smoothed particle hydrodynamics”, Adami, Hu, Adams, 2012

jax_sph.solver.gwbc_fn_riemann_wrapper(is_free_slip, is_heat_conduction)

Riemann solver boundary condition for wall particles.

jax_sph.solver.limiter_fn_wrapper(eta_limiter, c_ref)

if eta_limiter != -1, introduce dissipation limiter eq. (11), Zhang (2017).

jax_sph.solver.temperature_derivative_wrapper(kernel_fn)

Temperature derivative according to Cleary 1998.

class jax_sph.solver.WCSPH(displacement_fn: Callable, eos: TaitEoS | RIEMANNEoS, g_ext_fn: Callable, dx: float, dim: int, dt: float, c_ref: float, eta_limiter: float = 3, solver: str = 'SPH', kernel: str = 'QSK', is_bc_trick: bool = False, is_rho_evol: bool = False, artificial_alpha: float = 0.0, is_free_slip: bool = False, is_rho_renorm: bool = False, is_heat_conduction: bool = False)

Weakly compressible SPH solver with transport velocity formulation.

forward_wrapper()

Wrapper of update step of SPH.

Equation of State

Equation of state.

class jax_sph.eos.BaseEoS

Base class for SPH equation of state.

abstract p_fn(rho: float)

Compute pressure from density.

abstract rho_fn(p: float)

Compute density from pressure.

class jax_sph.eos.TaitEoS(p_ref, rho_ref, p_background, gamma)

Tait equation of state.

From: “A generalized wall boundary condition for smoothed particle hydrodynamics”, Adami et al 2012

p_fn(rho)

Compute pressure from density.

rho_fn(p)

Compute density from pressure.

class jax_sph.eos.RIEMANNEoS(rho_ref, p_background, u_ref)

Riemann SPH equation of state.

From: “A weakly compressible SPH method based on a low-dissipation Riemann solver”, Zhang, Hu, Adams, 2017

p_fn(rho)

Compute pressure from density.

rho_fn(p)

Compute density from pressure.

Kernels

SPH interpolation kernels.

class jax_sph.kernel.BaseKernel(h: float)

Base class for SPH interpolation kernels.

abstract w(r)

Evaluates the kernel at the radial distance r.

grad_w(r)

Evaluates the 1D kernel gradient at the radial distance r.

class jax_sph.kernel.CubicKernel(h, dim=3)

The cubic kernel function of Monaghan.

w(r)

Evaluates the kernel at the radial distance r.

class jax_sph.kernel.QuinticKernel(h, dim=3)

The quintic kernel function of Morris.

w(r)

Evaluates the kernel at the radial distance r.

class jax_sph.kernel.WendlandC2Kernel(h, dim=3)

The 5th-order C2 kernel function of Wendland.

w(r)

Evaluates the kernel at the radial distance r.

class jax_sph.kernel.WendlandC4Kernel(h, dim=3)

The 5th-order C4 kernel function of Wendland.

w(r)

Evaluates the kernel at the radial distance r.

class jax_sph.kernel.WendlandC6Kernel(h, dim=3)

The 5th-order C6 kernel function of Wendland.

w(r)

Evaluates the kernel at the radial distance r.

class jax_sph.kernel.GaussianKernel(h, dim=3)

The gaussian kernel function of Monaghan.

w(r)

Evaluates the kernel at the radial distance r.

class jax_sph.kernel.SuperGaussianKernel(h, dim=3)

The supergaussian kernel function of Monaghan.

w(r)

Evaluates the kernel at the radial distance r.

Integrator

Integrator schemes.

jax_sph.integrator.si_euler(tvf: float, model: Callable, shift_fn: Callable, bc_fn: Callable, nw_fn: Callable)

Semi-implicit Euler integrator including Transport Velocity.

The integrator advances the state of the system following the steps:

1. Update u and v with dudt and dvdt

2. Update position r with velocity v

3. Update neighbor list

4. Compute accelerations - SPH model call

5. Impose boundary conditions as defined by the case.