working delta-sph and fix usage of "h_factor"

jax_sph/case_setup.py

@@ -187,7 +187,7 @@ def initialize(self):
                 if k not in cfg.case.state0_keys:
                     continue
                 assert k in _state, ValueError(f"Key {k} not found in state0 file.")
-                mask, _mask = state["tag"]==Tag.FLUID, _state["tag"]==Tag.FLUID
+                mask, _mask = state["tag"] == Tag.FLUID, _state["tag"] == Tag.FLUID
                 assert state[k][mask].shape == _state[k][_mask].shape, ValueError(
                     f"Shape mismatch for key {k} in state0 file."
                 )

jax_sph/defaults.py

@@ -64,7 +64,8 @@ def set_defaults(cfg: DictConfig = OmegaConf.create({})) -> DictConfig:
     ### solver
     cfg.solver = OmegaConf.create({})
 
-    # Solver name. One of "SPH" (standard SPH) or "RIE" (Riemann SPH)
+    # Solver name. One of "SPH" (standard SPH) or "RIE" (Riemann SPH) or
+    # "DELTA" (Delta SPH)
     cfg.solver.name = "SPH"
     # Transport velocity inclusion factor [0,...,1]
     cfg.solver.tvf = 0.0
@@ -92,6 +93,10 @@ def set_defaults(cfg: DictConfig = OmegaConf.create({})) -> DictConfig:
     cfg.solver.heat_conduction = False
     # Whether to apply boundaty conditions
     cfg.solver.is_bc_trick = False  # new
+    # Delta SPH density diffusion weighting factor
+    cfg.solver.diff_delta = 0.1
+    # Delta SPH acceleratin diffusion weighting factor
+    cfg.solver.diff_alpha = 0.01
 
     ### kernel
     cfg.kernel = OmegaConf.create({})
@@ -105,8 +110,10 @@ def set_defaults(cfg: DictConfig = OmegaConf.create({})) -> DictConfig:
     # "GK" (gaussian kernel)
     # "SGK" (super gaussian kernel)
     cfg.kernel.name = "QSK"
-    # Smoothing length factor
-    cfg.kernel.h_factor = 1.0  # new. Should default to 1.3 WC2K and 1.0 QSK
+    # Smoothing length factor, should default to
+    # 1.3 for WC2K, WC4K, WC6K
+    # 1.0 for CSK, QSK, GK, SGK
+    cfg.kernel.h_factor = 1.0
 
     ### equation of state
     cfg.eos = OmegaConf.create({})

jax_sph/simulate.py

@@ -55,8 +55,11 @@ def simulate(cfg: DictConfig):
         cfg.solver.dt,
         cfg.case.c_ref,
         cfg.solver.eta_limiter,
+        cfg.solver.diff_delta,
+        cfg.solver.diff_alpha,
         cfg.solver.name,
         cfg.kernel.name,
+        cfg.kernel.h_factor,
         cfg.solver.is_bc_trick,
         cfg.solver.density_evolution,
         cfg.solver.artificial_alpha,

jax_sph/solver.py

@@ -30,6 +30,81 @@ def rho_evol_fn(rho, mass, u, grad_w_dist, i_s, j_s, dt, N, **kwargs):
     return rho, drhodt
 
 
+def rho_evol_fn_delta_wrapper(delta, support, c_ref, kernel_fn):
+    """Density evolution according to Marrone et al. 2011."""
+
+    def rho_evol_fn_delta(
+        rho, mass, r_ij, d_ij, u, i_s, j_s, dt, N, fluidmask_j, **kwargs
+    ):
+        # compute common quantities
+        def quantities_fn(r_ab, d_ab, m_a, m_b, rho_a, rho_b):
+            e_ab = r_ab / (d_ab + EPS)
+            kernel_grad = kernel_fn.grad_w(d_ab) * (e_ab)
+            V_a = m_a / rho_a
+            V_b = m_b / rho_b
+            return kernel_grad, V_a, V_b
+
+        kernel_grad, V_i, V_j = vmap(quantities_fn)(
+            r_ij, d_ij, mass[i_s], mass[j_s], rho[i_s], rho[j_s]
+        )
+
+        def L_fn(r_ab, kernel_grad, V_b):
+            return jnp.tensordot(-r_ab, kernel_grad * V_b, axes=0)
+
+        temp = vmap(L_fn)(r_ij, kernel_grad, V_j)
+        L_mati = jnp.linalg.inv(ops.segment_sum(temp, i_s, N))
+        temp = vmap(L_fn)(-r_ij, kernel_grad, V_i)
+        L_matj = jnp.linalg.inv(ops.segment_sum(temp, j_s, N))
+
+        def rho_grad_fn(rho_a, rho_b, L_a, kernel_grad, V_b):
+            return (rho_b - rho_a) * jnp.dot(L_a, kernel_grad * V_b)
+
+        temp = vmap(rho_grad_fn)(rho[i_s], rho[j_s], L_mati[i_s], kernel_grad, V_j)
+        rho_grad_term_i = ops.segment_sum(temp, i_s, N)
+        temp = vmap(rho_grad_fn)(rho[j_s], rho[i_s], L_matj[j_s], -kernel_grad, V_i)
+        rho_grad_term_j = ops.segment_sum(temp, i_s, N)
+
+        def rho_diff_fn(
+            rho_i,
+            rho_j,
+            r_ij,
+            d_ij,
+            rho_grad_term_i,
+            rho_grad_term_j,
+            fluidmask_j,
+            kernel_grad,
+            V_j,
+        ):
+            rho_term = 2 * (rho_j - rho_i) * (-r_ij) / (d_ij + EPS) ** 2
+            psi_ij = rho_term - rho_grad_term_i - rho_grad_term_j
+            return jnp.dot(psi_ij, kernel_grad) * V_j * fluidmask_j
+
+        temp = vmap(rho_diff_fn)(
+            rho[i_s],
+            rho[j_s],
+            r_ij,
+            d_ij,
+            rho_grad_term_i[i_s],
+            rho_grad_term_j[j_s],
+            fluidmask_j,
+            kernel_grad,
+            V_j,
+        )
+        diff_term = ops.segment_sum(temp, i_s, N)
+
+        def cont_eq(u_i, u_j, kernel_grad, V_j):
+            return jnp.dot(u_i - u_j, kernel_grad) * V_j
+
+        temp = vmap(cont_eq)(u[i_s], u[j_s], kernel_grad, V_j)
+        drhodt = (
+            rho * ops.segment_sum(temp, i_s, N) + c_ref * delta * support * diff_term
+        )
+        rho = rho + dt * drhodt
+        return rho, drhodt
+
+    return rho_evol_fn_delta
+
+
 def rho_evol_riemann_fn_wrapper(kernel_fn, eos, c_ref):
     """Density evolution according to Zhang et al. 2017."""
 
@@ -181,6 +256,63 @@ def acceleration_standard_fn(
     return acceleration_standard_fn
 
 
+def acceleration_delta_fn_wrapper(kernel_fn, alpha, support, c_ref, rho_ref):
+    """Standard SPH acceleration according to Adami et al. 2012., and
+    Delta SPH relaxation according to Marrone et al. 2011."""
+
+    def acceleration_delta_fn(
+        r_ij,
+        d_ij,
+        rho_i,
+        rho_j,
+        u_i,
+        u_j,
+        v_i,
+        v_j,
+        m_i,
+        m_j,
+        eta_i,
+        eta_j,
+        p_i,
+        p_j,
+        fluidmask_j,
+    ):
+        # (Eq. 6) - inter-particle-averaged shear viscosity (harmonic mean)
+        eta_ij = 2 * eta_i * eta_j / (eta_i + eta_j + EPS)
+        # (Eq. 7) - density-weighted pressure (weighted arithmetic mean)
+        p_ij = (rho_j * p_i + rho_i * p_j) / (rho_i + rho_j)
+
+        # compute the common prefactor `c`
+        weighted_volume = ((m_i / rho_i) ** 2 + (m_j / rho_j) ** 2) / m_i
+        kernel_grad = kernel_fn.grad_w(d_ij)
+        c = weighted_volume * kernel_grad / (d_ij + EPS)
+
+        # (Eq. 8): \boldsymbol{e}_{ij} is computed as r_ij/d_ij here.
+        _A = (tvf_stress_fn(rho_i, u_i, v_i) + tvf_stress_fn(rho_j, u_j, v_j)) / 2
+        _u_ij = u_i - u_j
+        a_eq_8 = c * (-p_ij * r_ij + jnp.dot(_A, r_ij) + eta_ij * _u_ij)
+
+        e_ij = r_ij / (d_ij + EPS)
+        kernel_grad = kernel_grad * (e_ij)
+        V_j = m_j / rho_j
+        pi_ij = jnp.dot((u_j - u_i), (-r_ij)) / (d_ij + EPS) ** 2
+        acceleration_diff = (
+            V_j
+            * pi_ij
+            * kernel_grad
+            * alpha
+            * support
+            * c_ref
+            * rho_ref
+            / rho_i
+            * fluidmask_j
+        )
+
+        return a_eq_8 + acceleration_diff
+
+    return acceleration_delta_fn
+
+
 def acceleration_riemann_fn_wrapper(kernel_fn, eos, beta_fn, eta_limiter):
     """Riemann solver acceleration according to Zhang et al. 2017."""
 
@@ -491,8 +623,11 @@ def __init__(
         dt: float,
         c_ref: float,
         eta_limiter: float = 3,
+        diff_delta: float = 0.02,
+        diff_alpha: float = 0.1,
         solver: str = "SPH",
         kernel: str = "QSK",
+        h_fac: float = 1.0,
         is_bc_trick: bool = False,
         is_rho_evol: bool = False,
         artificial_alpha: float = 0.0,
@@ -508,25 +643,27 @@ def __init__(
         self.is_rho_renorm = is_rho_renorm
         self.dt = dt
         self.eos = eos
+        self.c_ref = c_ref
+        self.diff_delta = diff_delta
+        self.diff_alpha = diff_alpha
         self.artificial_alpha = artificial_alpha
         self.is_heat_conduction = is_heat_conduction
 
         _beta_fn = limiter_fn_wrapper(eta_limiter, c_ref)
-        match kernel:
-            case "CSK":
-                self._kernel_fn = CubicKernel(h=dx, dim=dim)
-            case "QSK":
-                self._kernel_fn = QuinticKernel(h=dx, dim=dim)
-            case "WC2K":
-                self._kernel_fn = WendlandC2Kernel(h=1.3 * dx, dim=dim)
-            case "WC4K":
-                self._kernel_fn = WendlandC4Kernel(h=1.3 * dx, dim=dim)
-            case "WC6K":
-                self._kernel_fn = WendlandC6Kernel(h=1.3 * dx, dim=dim)
-            case "GK":
-                self._kernel_fn = GaussianKernel(h=dx, dim=dim)
-            case "SGK":
-                self._kernel_fn = SuperGaussianKernel(h=dx, dim=dim)
+        if kernel == "CSK":
+            self._kernel_fn = CubicKernel(h=h_fac * dx, dim=dim)
+        elif kernel == "QSK":
+            self._kernel_fn = QuinticKernel(h=h_fac * dx, dim=dim)
+        elif kernel == "WC2K":
+            self._kernel_fn = WendlandC2Kernel(h=h_fac * dx, dim=dim)
+        elif kernel == "WC4K":
+            self._kernel_fn = WendlandC4Kernel(h=h_fac * dx, dim=dim)
+        elif kernel == "WC6K":
+            self._kernel_fn = WendlandC6Kernel(h=h_fac * dx, dim=dim)
+        elif kernel == "GK":
+            self._kernel_fn = GaussianKernel(h=h_fac * dx, dim=dim)
+        elif kernel == "SGK":
+            self._kernel_fn = SuperGaussianKernel(h=h_fac * dx, dim=dim)
 
         self._gwbc_fn = gwbc_fn_wrapper(is_free_slip, is_heat_conduction, eos)
         (
@@ -535,17 +672,31 @@ def __init__(
             self._heat_bc,
         ) = gwbc_fn_riemann_wrapper(is_free_slip, is_heat_conduction)
         self._acceleration_tvf_fn = acceleration_tvf_fn_wrapper(self._kernel_fn)
-        self._acceleration_riemann_fn = acceleration_riemann_fn_wrapper(
-            self._kernel_fn, eos, _beta_fn, eta_limiter
-        )
-        self._acceleration_fn = acceleration_standard_fn_wrapper(self._kernel_fn)
+
+        if solver == "SPH":
+            self._acceleration_fn = acceleration_standard_fn_wrapper(self._kernel_fn)
+            self._rho_evol_fn = rho_evol_fn
+        elif solver == "RIE":
+            self._acceleration_fn = acceleration_riemann_fn_wrapper(
+                self._kernel_fn, eos, _beta_fn, eta_limiter
+            )
+            self._rho_evol_fn = rho_evol_riemann_fn_wrapper(self._kernel_fn, eos, c_ref)
+        elif solver == "DELTA":
+            self._acceleration_fn = acceleration_delta_fn_wrapper(
+                self._kernel_fn,
+                self.diff_alpha,
+                h_fac * dx,
+                self.c_ref,
+                self.eos.rho_ref,
+            )
+            self._rho_evol_fn = rho_evol_fn_delta_wrapper(
+                self.diff_delta, h_fac * dx, self.c_ref, self._kernel_fn
+            )
+
         self._artificial_viscosity_fn = artificial_viscosity_fn_wrapper(
             dx, artificial_alpha
         )
         self._wall_phi_vec = wall_phi_vec_wrapper(self._kernel_fn)
-        self._rho_evol_riemann_fn = rho_evol_riemann_fn_wrapper(
-            self._kernel_fn, eos, c_ref
-        )
         self._temperature_derivative = temperature_derivative_wrapper(self._kernel_fn)
 
     def forward_wrapper(self):
@@ -597,14 +748,29 @@ def forward(state, neighbors):
             # update evolution
 
             if self.is_rho_evol and (self.solver == "SPH"):
-                rho, drhodt = rho_evol_fn(
+                rho, drhodt = self._rho_evol_fn(
                     rho, mass, u, grad_w_dist, i_s, j_s, self.dt, N
                 )
 
+                if self.is_rho_renorm:
+                    rho = rho_renorm_fn(rho, mass, i_s, j_s, w_dist, N)
+            elif self.is_rho_evol and (self.solver == "DELTA"):
+                rho, drhodt = self._rho_evol_fn(
+                    rho,
+                    mass,
+                    dr_i_j,
+                    dist,
+                    u,
+                    i_s,
+                    j_s,
+                    self.dt,
+                    N,
+                    fluid_mask[j_s],
+                )
                 if self.is_rho_renorm:
                     rho = rho_renorm_fn(rho, mass, i_s, j_s, w_dist, N)
             elif self.is_rho_evol and (self.solver == "RIE"):
-                temp = vmap(self._rho_evol_riemann_fn)(
+                temp = vmap(self._rho_evol_fn)(
                     e_s,
                     rho[i_s],
                     rho[j_s],
@@ -637,7 +803,7 @@ def forward(state, neighbors):
 
             #####  Apply BC trick
 
-            if self.is_bc_trick and (self.solver == "SPH"):
+            if self.is_bc_trick and (self.solver == "SPH" or self.solver == "DELTA"):
                 p, rho, u, v, temperature = self._gwbc_fn(
                     temperature,
                     rho,
@@ -702,8 +868,26 @@ def forward(state, neighbors):
                     p[i_s],
                     p[j_s],
                 )
+            elif self.solver == "DELTA":
+                out = vmap(self._acceleration_fn)(
+                    dr_i_j,
+                    dist,
+                    rho[i_s],
+                    rho[j_s],
+                    u[i_s],
+                    u[j_s],
+                    v[i_s],
+                    v[j_s],
+                    mass[i_s],
+                    mass[j_s],
+                    eta[i_s],
+                    eta[j_s],
+                    p[i_s],
+                    p[j_s],
+                    fluid_mask[j_s],
+                )
             elif self.solver == "RIE":
-                out = vmap(self._acceleration_riemann_fn)(
+                out = vmap(self._acceleration_fn)(
                     e_s,
                     dr_i_j,
                     dist,

tests/test_pf2d.py

@@ -103,7 +103,9 @@ def get_solution(data_path, t_dimless, y_axis):
     return solutions
 
 
-@pytest.mark.parametrize("tvf, solver", [(0.0, "SPH"), (1.0, "SPH"), (0.0, "RIE")])
+@pytest.mark.parametrize(
+    "tvf, solver", [(0.0, "SPH"), (1.0, "SPH"), (0.0, "RIE"), (0.0, "DELTA")]
+)
 def test_pf2d(tvf, solver, tmp_path, setup_simulation):
     """Test whether the poiseuille flow simulation matches the analytical solution"""
     y_axis, t_dimless, ref_solutions = setup_simulation

validation/db2d.sh

@@ -1,7 +1,12 @@
 #!/bin/bash
 
 ####### 2D Dam break
+# Riemann SPH
 python main.py config=cases/db.yaml case.u_ref=2 case.viscosity=0.0 solver.name=RIE solver.t_end=7.5 solver.dt=0.0002 solver.free_slip=True solver.artificial_alpha=0.0 solver.eta_limiter=3 io.write_every=50 io.data_path=data_valid/db2d_Riemann/
 
+# Delta SPH
+python main.py config=cases/db.yaml case.u_ref=1.95 case.special.H_wall=5.366 case.viscosity=0.0 eos.gamma=7.0 solver.name=DELTA solver.t_end=7.5 solver.dt=0.0002 solver.free_slip=True solver.artificial_alpha=0.0 io.write_every=50 io.data_path=data_valid/db2d_Delta/
+
 # Run validation script
 python validation/validate.py --case=2D_DB --src_dir=data_valid/db2d_Riemann/
+python validation/validate.py --case=2D_DB --src_dir=data_valid/db2d_Delta/

validation/pf2d.sh

@@ -6,9 +6,11 @@
 # Generate data
 python main.py config=cases/pf.yaml solver.tvf=1.0 io.data_path=data_valid/pf2d_tvf/
 python main.py config=cases/pf.yaml solver.tvf=0.0 io.data_path=data_valid/pf2d_notvf/
+python main.py config=cases/pf.yaml solver.tvf=0.0 solver.name=DELTA io.data_path=data_valid/pf2d_delta/
 python main.py config=cases/pf.yaml solver.tvf=0.0 solver.name=RIE solver.density_evolution=True io.data_path=data_valid/pf2d_Rie/
 
 # Run validation script
 python validation/validate.py --case=2D_PF --src_dir=data_valid/pf2d_tvf/
 python validation/validate.py --case=2D_PF --src_dir=data_valid/pf2d_notvf/
+python validation/validate.py --case=2D_PF --src_dir=data_valid/pf2d_delta/
 python validation/validate.py --case=2D_PF --src_dir=data_valid/pf2d_Rie/