Add P-U with M&M Switch

configure.ac

@@ -1150,7 +1150,7 @@ esac
 # Hydro scheme.
 AC_ARG_WITH([hydro],
    [AS_HELP_STRING([--with-hydro=<scheme>],
-      [Hydro dynamics to use @<:@gadget2, minimal, pressure-entropy, pressure-energy, default, gizmo-mfv, gizmo-mfm, shadowfax, planetary, debug default: gadget2@:>@]
+      [Hydro dynamics to use @<:@gadget2, minimal, pressure-entropy, pressure-energy, pressure-energy-monaghan, default, gizmo-mfv, gizmo-mfm, shadowfax, planetary, debug default: gadget2@:>@]
    )],
    [with_hydro="$withval"],
    [with_hydro="gadget2"]
@@ -1177,6 +1177,9 @@ case "$with_hydro" in
    pressure-energy)
       AC_DEFINE([HOPKINS_PU_SPH], [1], [Pressure-Energy SPH])
    ;;
+   pressure-energy-monaghan)
+      AC_DEFINE([HOPKINS_PU_SPH_MONAGHAN], [1], [Pressure-Energy SPH with M&M Variable A.V.])
+   ;;
    default)
       AC_DEFINE([DEFAULT_SPH], [1], [Default SPH])
    ;;

examples/KelvinHelmholtz_2D/makeMovie.py

@@ -91,6 +91,7 @@ if __name__ == "__main__":
 
     # Creation of first frame
     fig, ax = plt.subplots(1, 1, figsize=(1, 1), frameon=False)
+    ax.axis("off")  # Remove annoying black frame.
 
     data_x, data_y, density = load_and_extract("kelvinhelmholtz_0000.hdf5")
 

examples/SodShock_1D/plotSolution.py

@@ -70,11 +70,11 @@ snap = int(sys.argv[1])
 sim = h5py.File("sodShock_%04d.hdf5"%snap, "r")
 boxSize = sim["/Header"].attrs["BoxSize"][0]
 time = sim["/Header"].attrs["Time"][0]
-scheme = sim["/HydroScheme"].attrs["Scheme"]
-kernel = sim["/HydroScheme"].attrs["Kernel function"]
+scheme = str(sim["/HydroScheme"].attrs["Scheme"])
+kernel = str(sim["/HydroScheme"].attrs["Kernel function"])
 neighbours = sim["/HydroScheme"].attrs["Kernel target N_ngb"]
 eta = sim["/HydroScheme"].attrs["Kernel eta"]
-git = sim["Code"].attrs["Git Revision"]
+git = str(sim["Code"].attrs["Git Revision"])
 
 x = sim["/PartType0/Coordinates"][:,0]
 v = sim["/PartType0/Velocities"][:,0]
@@ -82,6 +82,11 @@ u = sim["/PartType0/InternalEnergy"][:]
 S = sim["/PartType0/Entropy"][:]
 P = sim["/PartType0/Pressure"][:]
 rho = sim["/PartType0/Density"][:]
+try:
+    alpha = sim["/PartType0/Viscosity"][:]
+    plot_alpha = True 
+except:
+    plot_alpha = False
 
 N = 1000  # Number of points
 x_min = -1.
@@ -259,14 +264,23 @@ ylabel("${\\rm{Internal~Energy}}~u$", labelpad=0)
 xlim(-0.5, 0.5)
 ylim(0.8, 2.2)
 
-# Entropy profile ---------------------------------
+# Entropy/alpha profile ---------------------------------
 subplot(235)
-plot(x, S, '.', color='r', ms=4.0)
-plot(x_s, s_s, '--', color='k', alpha=0.8, lw=1.2)
+
+if plot_alpha:
+    plot(x, alpha, '.', color='r', ms=4.0)
+    ylabel(r"${\rm{Viscosity}}~\alpha$", labelpad=0)
+    # Show location of shock
+    plot([x_56, x_56], [-100, 100], color="k", alpha=0.5, ls="dashed", lw=1.2)
+    ylim(0, 1)
+else:
+    plot(x, S, '.', color='r', ms=4.0)
+    plot(x_s, s_s, '--', color='k', alpha=0.8, lw=1.2)
+    ylabel("${\\rm{Entropy}}~S$", labelpad=0)
+    ylim(0.8, 3.8)
+
 xlabel("${\\rm{Position}}~x$", labelpad=0)
-ylabel("${\\rm{Entropy}}~S$", labelpad=0)
 xlim(-0.5, 0.5)
-ylim(0.8, 3.8)
 
 # Information -------------------------------------
 subplot(236, frameon=False)
@@ -284,5 +298,6 @@ ylim(0, 1)
 xticks([])
 yticks([])
 
+tight_layout()
 
 savefig("SodShock.png", dpi=200)

src/debug.c

@@ -48,6 +48,8 @@
 #include "./hydro/PressureEntropy/hydro_debug.h"
 #elif defined(HOPKINS_PU_SPH)
 #include "./hydro/PressureEnergy/hydro_debug.h"
+#elif defined(HOPKINS_PU_SPH_MONAGHAN)
+#include "./hydro/PressureEnergyMorrisMonaghanAV/hydro_debug.h"
 #elif defined(DEFAULT_SPH)
 #include "./hydro/Default/hydro_debug.h"
 #elif defined(GIZMO_MFV_SPH)

src/hydro.h

@@ -45,6 +45,12 @@
 #include "./hydro/PressureEnergy/hydro.h"
 #include "./hydro/PressureEnergy/hydro_iact.h"
 #define SPH_IMPLEMENTATION "Pressure-Energy SPH (Hopkins 2013)"
+#elif defined(HOPKINS_PU_SPH_MONAGHAN)
+#include "./hydro/PressureEnergyMorrisMonaghanAV/hydro.h"
+#include "./hydro/PressureEnergyMorrisMonaghanAV/hydro_iact.h"
+#define SPH_IMPLEMENTATION                                                \
+  "Pressure-Energy SPH (Hopkins 2013) with a Morris and Monaghan (1997) " \
+  "variable artificial viscosity."
 #elif defined(DEFAULT_SPH)
 #include "./hydro/Default/hydro.h"
 #include "./hydro/Default/hydro_iact.h"

src/hydro/PressureEnergy/hydro.h

@@ -472,8 +472,10 @@ __attribute__((always_inline)) INLINE static void hydro_end_density(
   p->density.rot_v[1] *= h_inv_dim_plus_one * a_inv2 * rho_inv;
   p->density.rot_v[2] *= h_inv_dim_plus_one * a_inv2 * rho_inv;
 
-  /* Finish calculation of the velocity divergence */
-  p->density.div_v *= h_inv_dim_plus_one * rho_inv * a_inv2;
+  /* Finish calculation of the velocity divergence, including hubble flow term
+   */
+  p->density.div_v *=
+      h_inv_dim_plus_one * rho_inv * a_inv2 + cosmo->H * hydro_dimension;
 }
 
 /**

src/hydro/PressureEnergy/hydro_iact.h

@@ -284,7 +284,7 @@ __attribute__((always_inline)) INLINE static void runner_iact_force(
                               wj_dr * dvdr * r_inv;
 
   /* Viscosity term */
-  const float visc_du_term = 0.5f * visc_acc_term * dvdr;
+  const float visc_du_term = 0.5f * visc_acc_term * dvdr_Hubble;
 
   /* Assemble the energy equation term */
   const float du_dt_i = sph_du_term_i + visc_du_term;
@@ -404,7 +404,7 @@ __attribute__((always_inline)) INLINE static void runner_iact_nonsym_force(
                               wi_dr * dvdr * r_inv;
 
   /* Viscosity term */
-  const float visc_du_term = 0.5f * visc_acc_term * dvdr;
+  const float visc_du_term = 0.5f * visc_acc_term * dvdr_Hubble;
 
   /* Assemble the energy equation term */
   const float du_dt_i = sph_du_term_i + visc_du_term;

src/hydro/PressureEnergyMorrisMonaghanAV/hydro_debug.h

+/*******************************************************************************
+ * This file is part of SWIFT.
+ * Coypright (c) 2016 Matthieu Schaller (matthieu.schaller@durham.ac.uk) &
+ *                    Josh Borrow (joshua.borrow@durham.ac.uk)
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU Lesser General Public License as published
+ * by the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public License
+ * along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ *
+ ******************************************************************************/
+#ifndef SWIFT_PRESSURE_ENERGY_MORRIS_HYDRO_DEBUG_H
+#define SWIFT_PRESSURE_ENERGY_MORRIS_HYDRO_DEBUG_H
+/**
+ * @file PressureEnergy/hydro_debug.h
+ * @brief P-U conservative implementation of SPH (Debugging routines)
+ *
+ * The thermal variable is the internal energy (u). A simple variable
+ * viscosity term (Morris & Monaghan 1997) with a Balsara switch is
+ * implemented.
+ */
+
+__attribute__((always_inline)) INLINE static void hydro_debug_particle(
+    const struct part* p, const struct xpart* xp) {
+  printf(
+      "x=[%.3e,%.3e,%.3e], "
+      "v=[%.3e,%.3e,%.3e],v_full=[%.3e,%.3e,%.3e] \n a=[%.3e,%.3e,%.3e], "
+      "u=%.3e, du/dt=%.3e v_sig=%.3e, P=%.3e\n"
+      "h=%.3e, dh/dt=%.3e wcount=%d, m=%.3e, dh_drho=%.3e, rho=%.3e, \n"
+      "p_dh=%.3e, p_bar=%.3e \n"
+      "time_bin=%d, alpha=%.3e\n",
+      p->x[0], p->x[1], p->x[2], p->v[0], p->v[1], p->v[2], xp->v_full[0],
+      xp->v_full[1], xp->v_full[2], p->a_hydro[0], p->a_hydro[1], p->a_hydro[2],
+      p->u, p->u_dt, p->force.v_sig, hydro_get_comoving_pressure(p), p->h,
+      p->force.h_dt, (int)p->density.wcount, p->mass, p->density.rho_dh, p->rho,
+      p->density.pressure_bar_dh, p->pressure_bar, p->time_bin, p->alpha);
+}
+
+#endif /* SWIFT_PRESSURE_ENERGY_MORRIS_HYDRO_DEBUG_H */

src/hydro/PressureEnergyMorrisMonaghanAV/hydro_iact.h

+/*******************************************************************************
+ * This file is part* of SWIFT.
+ * Copyright (c) 2016 Matthieu Schaller (matthieu.schaller@durham.ac.uk) &
+ *                    Josh Borrow (joshua.borrow@durham.ac.uk)
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU Lesser General Public License as published
+ * by the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public License
+ * along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ *
+ ******************************************************************************/
+#ifndef SWIFT_PRESSURE_ENERGY_MORRIS_HYDRO_IACT_H
+#define SWIFT_PRESSURE_ENERGY_MORRIS_HYDRO_IACT_H
+
+/**
+ * @file PressureEnergy/hydro_iact.h
+ * @brief P-U implementation of SPH (Neighbour loop equations)
+ *
+ * The thermal variable is the internal energy (u). A simple variable
+ * viscosity term (Morris & Monaghan 1997) with a Balsara switch is
+ * implemented.
+ *
+ * No thermal conduction term is implemented.
+ *
+ * See PressureEnergy/hydro.h for references.
+ */
+
+#include "adiabatic_index.h"
+#include "minmax.h"
+
+/**
+ * @brief Density interaction between two part*icles.
+ *
+ * @param r2 Comoving square distance between the two part*icles.
+ * @param dx Comoving vector separating both part*icles (pi - pj).
+ * @param hi Comoving smoothing-length of part*icle i.
+ * @param hj Comoving smoothing-length of part*icle j.
+ * @param pi First part*icle.
+ * @param pj Second part*icle.
+ * @param a Current scale factor.
+ * @param H Current Hubble parameter.
+ */
+__attribute__((always_inline)) INLINE static void runner_iact_density(
+    float r2, const float* dx, float hi, float hj, struct part* pi,
+    struct part* pj, float a, float H) {
+
+  float wi, wj, wi_dx, wj_dx;
+  float dv[3], curlvr[3];
+
+  const float r = sqrtf(r2);
+
+  /* Get the masses. */
+  const float mi = pi->mass;
+  const float mj = pj->mass;
+
+  /* Compute density of pi. */
+  const float hi_inv = 1.f / hi;
+  const float ui = r * hi_inv;
+
+  kernel_deval(ui, &wi, &wi_dx);
+
+  pi->rho += mj * wi;
+  pi->density.rho_dh -= mj * (hydro_dimension * wi + ui * wi_dx);
+
+  pi->pressure_bar += mj * wi * pj->u;
+  pi->density.pressure_bar_dh -=
+      mj * pj->u * (hydro_dimension * wi + ui * wi_dx);
+  pi->density.wcount += wi;
+  pi->density.wcount_dh -= (hydro_dimension * wi + ui * wi_dx);
+
+  /* Compute density of pj. */
+  const float hj_inv = 1.f / hj;
+  const float uj = r * hj_inv;
+  kernel_deval(uj, &wj, &wj_dx);
+
+  pj->rho += mi * wj;
+  pj->density.rho_dh -= mi * (hydro_dimension * wj + uj * wj_dx);
+  pj->pressure_bar += mi * wj * pi->u;
+  pj->density.pressure_bar_dh -=
+      mi * pi->u * (hydro_dimension * wj + uj * wj_dx);
+  pj->density.wcount += wj;
+  pj->density.wcount_dh -= (hydro_dimension * wj + uj * wj_dx);
+
+  /* Now we need to compute the div terms */
+  const float r_inv = 1.f / r;
+  const float faci = mj * wi_dx * r_inv;
+  const float facj = mi * wj_dx * r_inv;
+
+  /* Compute dv dot r */
+  dv[0] = pi->v[0] - pj->v[0];
+  dv[1] = pi->v[1] - pj->v[1];
+  dv[2] = pi->v[2] - pj->v[2];
+  const float dvdr = dv[0] * dx[0] + dv[1] * dx[1] + dv[2] * dx[2];
+
+  pi->density.div_v -= faci * dvdr;
+  pj->density.div_v -= facj * dvdr;
+
+  /* Compute dv cross r */
+  curlvr[0] = dv[1] * dx[2] - dv[2] * dx[1];
+  curlvr[1] = dv[2] * dx[0] - dv[0] * dx[2];
+  curlvr[2] = dv[0] * dx[1] - dv[1] * dx[0];
+
+  pi->density.rot_v[0] += faci * curlvr[0];
+  pi->density.rot_v[1] += faci * curlvr[1];
+  pi->density.rot_v[2] += faci * curlvr[2];
+
+  /* Negative because of the change in sign of dx & dv. */
+  pj->density.rot_v[0] += facj * curlvr[0];
+  pj->density.rot_v[1] += facj * curlvr[1];
+  pj->density.rot_v[2] += facj * curlvr[2];
+}
+
+/**
+ * @brief Density interaction between two part*icles (non-symmetric).
+ *
+ * @param r2 Comoving square distance between the two part*icles.
+ * @param dx Comoving vector separating both part*icles (pi - pj).
+ * @param hi Comoving smoothing-length of part*icle i.
+ * @param hj Comoving smoothing-length of part*icle j.
+ * @param pi First part*icle.
+ * @param pj Second part*icle (not updated).
+ * @param a Current scale factor.
+ * @param H Current Hubble parameter.
+ */
+__attribute__((always_inline)) INLINE static void runner_iact_nonsym_density(
+    float r2, const float* dx, float hi, float hj, struct part* pi,
+    const struct part* pj, float a, float H) {
+
+  float wi, wi_dx;
+  float dv[3], curlvr[3];
+
+  /* Get the masses. */
+  const float mj = pj->mass;
+
+  /* Get r and r inverse. */
+  const float r = sqrtf(r2);
+
+  const float h_inv = 1.f / hi;
+  const float ui = r * h_inv;
+  kernel_deval(ui, &wi, &wi_dx);
+
+  pi->rho += mj * wi;
+  pi->density.rho_dh -= mj * (hydro_dimension * wi + ui * wi_dx);
+
+  pi->pressure_bar += mj * wi * pj->u;
+
+  pi->density.pressure_bar_dh -=
+      mj * pj->u * (hydro_dimension * wi + ui * wi_dx);
+  pi->density.wcount += wi;
+  pi->density.wcount_dh -= (hydro_dimension * wi + ui * wi_dx);
+
+  const float r_inv = 1.f / r;
+  const float faci = mj * wi_dx * r_inv;
+
+  /* Compute dv dot r */
+  dv[0] = pi->v[0] - pj->v[0];
+  dv[1] = pi->v[1] - pj->v[1];
+  dv[2] = pi->v[2] - pj->v[2];
+  const float dvdr = dv[0] * dx[0] + dv[1] * dx[1] + dv[2] * dx[2];
+
+  pi->density.div_v -= faci * dvdr;
+
+  /* Compute dv cross r */
+  curlvr[0] = dv[1] * dx[2] - dv[2] * dx[1];
+  curlvr[1] = dv[2] * dx[0] - dv[0] * dx[2];
+  curlvr[2] = dv[0] * dx[1] - dv[1] * dx[0];
+
+  pi->density.rot_v[0] += faci * curlvr[0];
+  pi->density.rot_v[1] += faci * curlvr[1];
+  pi->density.rot_v[2] += faci * curlvr[2];
+}
+
+/**
+ * @brief Force interaction between two part*icles.
+ *
+ * @param r2 Comoving square distance between the two part*icles.
+ * @param dx Comoving vector separating both part*icles (pi - pj).
+ * @param hi Comoving smoothing-length of part*icle i.
+ * @param hj Comoving smoothing-length of part*icle j.
+ * @param pi First part*icle.
+ * @param pj Second part*icle.
+ * @param a Current scale factor.
+ * @param H Current Hubble parameter.
+ */
+__attribute__((always_inline)) INLINE static void runner_iact_force(
+    float r2, const float* dx, float hi, float hj, struct part* pi,
+    struct part* pj, float a, float H) {
+
+  /* Cosmological factors entering the EoMs */
+  const float fac_mu = pow_three_gamma_minus_five_over_two(a);
+  const float a2_Hubble = a * a * H;
+
+  const float r = sqrtf(r2);
+  const float r_inv = 1.0f / r;
+
+  /* Recover some data */
+  const float mj = pj->mass;
+  const float mi = pi->mass;
+
+  const float miui = mi * pi->u;
+  const float mjuj = mj * pj->u;
+
+  const float rhoi = pi->rho;
+  const float rhoj = pj->rho;
+  /* Compute gradient terms */
+  const float f_ij = 1.f - (pi->force.f / mjuj);
+  const float f_ji = 1.f - (pj->force.f / miui);
+
+  /* Get the kernel for hi. */
+  const float hi_inv = 1.0f / hi;
+  const float hid_inv = pow_dimension_plus_one(hi_inv); /* 1/h^(d+1) */
+  const float xi = r * hi_inv;
+  float wi, wi_dx;
+  kernel_deval(xi, &wi, &wi_dx);
+  const float wi_dr = hid_inv * wi_dx;
+
+  /* Get the kernel for hj. */
+  const float hj_inv = 1.0f / hj;
+  const float hjd_inv = pow_dimension_plus_one(hj_inv); /* 1/h^(d+1) */
+  const float xj = r * hj_inv;
+  float wj, wj_dx;
+  kernel_deval(xj, &wj, &wj_dx);
+  const float wj_dr = hjd_inv * wj_dx;
+
+  /* Compute dv dot r. */
+  const float dvdr = (pi->v[0] - pj->v[0]) * dx[0] +
+                     (pi->v[1] - pj->v[1]) * dx[1] +
+                     (pi->v[2] - pj->v[2]) * dx[2];
+
+  /* Includes the hubble flow term; not used for du/dt */
+  const float dvdr_Hubble = dvdr + a2_Hubble * r2;
+
+  /* Are the part*icles moving towards each others ? */
+  const float omega_ij = min(dvdr_Hubble, 0.f);
+  const float mu_ij = fac_mu * r_inv * omega_ij; /* This is 0 or negative */
+
+  /* Compute sound speeds and signal velocity */
+  const float ci = pi->force.soundspeed;
+  const float cj = pj->force.soundspeed;
+  const float v_sig = ci + cj - 3.f * mu_ij;
+
+  /* Balsara term */
+  const float balsara_i = pi->force.balsara;
+  const float balsara_j = pj->force.balsara;
+
+  /* Construct the full viscosity term */
+  const float rho_ij = 0.5f * (rhoi + rhoj);
+  const float alpha = 0.5f * (pi->alpha + pj->alpha);
+  const float visc =
+      -0.25f * alpha * v_sig * mu_ij * (balsara_i + balsara_j) / rho_ij;
+
+  /* Convolve with the kernel */
+  const float visc_acc_term = 0.5f * visc * (wi_dr + wj_dr) * r_inv;
+
+  /* SPH acceleration term */
+  const float sph_acc_term =
+      pj->u * pi->u * hydro_gamma_minus_one * hydro_gamma_minus_one *
+      ((f_ij / pi->pressure_bar) * wi_dr + (f_ji / pj->pressure_bar) * wj_dr) *
+      r_inv;
+
+  /* Assemble the acceleration */
+  const float acc = sph_acc_term + visc_acc_term;
+
+  /* Use the force Luke ! */
+  pi->a_hydro[0] -= mj * acc * dx[0];
+  pi->a_hydro[1] -= mj * acc * dx[1];
+  pi->a_hydro[2] -= mj * acc * dx[2];
+
+  pj->a_hydro[0] += mi * acc * dx[0];
+  pj->a_hydro[1] += mi * acc * dx[1];
+  pj->a_hydro[2] += mi * acc * dx[2];
+
+  /* Get the time derivative for u. */
+  const float sph_du_term_i = hydro_gamma_minus_one * hydro_gamma_minus_one *
+                              pj->u * pi->u * (f_ij / pi->pressure_bar) *
+                              wi_dr * dvdr * r_inv;
+  const float sph_du_term_j = hydro_gamma_minus_one * hydro_gamma_minus_one *
+                              pi->u * pj->u * (f_ji / pj->pressure_bar) *
+                              wj_dr * dvdr * r_inv;
+
+  /* Viscosity term */
+  const float visc_du_term = 0.5f * visc_acc_term * dvdr_Hubble;
+
+  /* Assemble the energy equation term */
+  const float du_dt_i = sph_du_term_i + visc_du_term;
+  const float du_dt_j = sph_du_term_j + visc_du_term;
+
+  /* Internal energy time derivative */
+  pi->u_dt += du_dt_i * mj;
+  pj->u_dt += du_dt_j * mi;
+
+  /* Get the time derivative for h. */
+  pi->force.h_dt -= mj * dvdr * r_inv / rhoj * wi_dr;
+  pj->force.h_dt -= mi * dvdr * r_inv / rhoi * wj_dr;
+
+  /* Update the signal velocity. */
+  pi->force.v_sig = max(pi->force.v_sig, v_sig);
+  pj->force.v_sig = max(pj->force.v_sig, v_sig);
+}
+
+/**
+ * @brief Force interaction between two part*icles (non-symmetric).
+ *
+ * @param r2 Comoving square distance between the two part*icles.
+ * @param dx Comoving vector separating both part*icles (pi - pj).
+ * @param hi Comoving smoothing-length of part*icle i.
+ * @param hj Comoving smoothing-length of part*icle j.
+ * @param pi First part*icle.
+ * @param pj Second part*icle (not updated).
+ * @param a Current scale factor.
+ * @param H Current Hubble parameter.
+ */
+__attribute__((always_inline)) INLINE static void runner_iact_nonsym_force(
+    float r2, const float* dx, float hi, float hj, struct part* pi,
+    const struct part* pj, float a, float H) {
+
+  /* Cosmological factors entering the EoMs */
+  const float fac_mu = pow_three_gamma_minus_five_over_two(a);
+  const float a2_Hubble = a * a * H;
+
+  const float r = sqrtf(r2);
+  const float r_inv = 1.0f / r;
+
+  /* Recover some data */
+  // const float mi = pi->mass;
+  const float mj = pj->mass;
+  const float mi = pi->mass;
+
+  const float miui = mi * pi->u;
+  const float mjuj = mj * pj->u;
+
+  const float rhoi = pi->rho;
+  const float rhoj = pj->rho;
+  /* Compute gradient terms */
+  const float f_ij = 1.f - (pi->force.f / mjuj);
+  const float f_ji = 1.f - (pj->force.f / miui);
+
+  /* Get the kernel for hi. */
+  const float hi_inv = 1.0f / hi;
+  const float hid_inv = pow_dimension_plus_one(hi_inv); /* 1/h^(d+1) */
+  const float xi = r * hi_inv;
+  float wi, wi_dx;
+  kernel_deval(xi, &wi, &wi_dx);
+  const float wi_dr = hid_inv * wi_dx;
+
+  /* Get the kernel for hj. */
+  const float hj_inv = 1.0f / hj;
+  const float hjd_inv = pow_dimension_plus_one(hj_inv); /* 1/h^(d+1) */
+  const float xj = r * hj_inv;
+  float wj, wj_dx;
+  kernel_deval(xj, &wj, &wj_dx);
+  const float wj_dr = hjd_inv * wj_dx;
+
+  /* Compute dv dot r. */
+  const float dvdr = (pi->v[0] - pj->v[0]) * dx[0] +
+                     (pi->v[1] - pj->v[1]) * dx[1] +
+                     (pi->v[2] - pj->v[2]) * dx[2];
+
+  /* Includes the hubble flow term; not used for du/dt */
+  const float dvdr_Hubble = dvdr + a2_Hubble * r2;
+
+  /* Are the part*icles moving towards each others ? */
+  const float omega_ij = min(dvdr_Hubble, 0.f);
+  const float mu_ij = fac_mu * r_inv * omega_ij; /* This is 0 or negative */
+
+  /* Compute sound speeds and signal velocity */
+  const float ci = pi->force.soundspeed;
+  const float cj = pj->force.soundspeed;
+  const float v_sig = ci + cj - 3.f * mu_ij;
+
+  /* Balsara term */
+  const float balsara_i = pi->force.balsara;
+  const float balsara_j = pj->force.balsara;
+
+  /* Construct the full viscosity term */
+  const float rho_ij = 0.5f * (rhoi + rhoj);
+  const float alpha = 0.5f * (pi->alpha + pj->alpha);
+  const float visc =
+      -0.25f * alpha * v_sig * mu_ij * (balsara_i + balsara_j) / rho_ij;