Add viscosity convergence test

.github/workflows/ci.yml

@@ -54,6 +54,7 @@ jobs:
             build/tst/regression/outputs/cluster_tabular_cooling/convergence.png
             build/tst/regression/outputs/aniso_therm_cond_ring_conv/ring_convergence.png
             build/tst/regression/outputs/aniso_therm_cond_gauss_conv/cond.png
+            build/tst/regression/outputs/viscosity/visc.png
             build/tst/regression/outputs/field_loop/field_loop.png
             build/tst/regression/outputs/riemann_hydro/shock_tube.png
             build/tst/regression/outputs/turbulence/parthenon.hst

inputs/viscosity.in

@@ -0,0 +1,73 @@
+# AthenaPK - a performance portable block structured AMR MHD code
+# Copyright (c) 2021, Athena Parthenon Collaboration. All rights reserved.
+# Licensed under the BSD 3-Clause License (the "LICENSE");
+
+<comment>
+problem   = Thermal diffusion setup
+
+<job>
+problem_id = visc
+
+<problem/visc>
+t0 = 0.5      # Temporal offset for initial Gaussian profile
+amp = 1e-6    # Amplitude of Gaussian profile
+
+<parthenon/mesh>
+refinement = none
+nghost = 2
+
+nx1 = 256
+x1min = -6.0
+x1max = 6.0
+ix1_bc = outflow
+ox1_bc = outflow
+
+nx2 = 1
+x2min = -1.0
+x2max = 1.0
+ix2_bc = periodic
+ox2_bc = periodic
+
+nx3 = 1
+x3min = -1.0
+x3max = 1.0
+ix3_bc = periodic
+ox3_bc = periodic
+
+<parthenon/meshblock>
+nx1=32
+nx2=1 
+nx3=1
+
+<parthenon/time>
+integrator = rk2
+# TODO(pgrete) figure out why such a low cfl is required to keep density and pressure positive
+# Is this related to/happening at the boundaries?
+# Does it also happen for Athena++ (need to disable implicit floors there)
+# Is it related to the ideal EOS (instead of isothermal) and/or Riemann solver?
+# Why do larger cfl work for rkl2 integrator?
+cfl = 0.1
+tlim = 2.0
+nlim = -1
+
+<hydro>
+fluid = euler
+riemann = hllc
+eos = adiabatic
+reconstruction = plm
+gamma = 1.4
+pfloor = 1e-12
+dfloor = 1e-12
+
+<diffusion>
+integrator = rkl2
+viscosity = isotropic
+viscosity_coeff = fixed
+mom_diff_coeff_code = 0.25
+#rkl2_max_dt_ratio = 200.0
+
+<parthenon/output0>
+file_type = hdf5
+dt = 2.0
+variables = prim
+id = prim

src/pgen/visc.cpp

@@ -27,10 +27,11 @@ void ProblemGenerator(MeshBlock *pmb, ParameterInput *pin) {
   auto &mbd = pmb->meshblock_data.Get();
   auto &u = mbd->Get("cons").data;
 
-  Real gm1 = pin->GetReal("hydro", "gamma") - 1.0;
+  auto gamma = pin->GetReal("hydro", "gamma");
+  auto gm1 = gamma - 1.0;
   Real v1 = 0., v2 = 0., v3 = 0.;
   Real d0 = 1.;
-  Real p0 = 1.;
+  Real p0 = d0 / gamma; // i.e., c_s = 1
   auto amp = pin->GetOrAddReal("problem/visc", "amp", 1.e-6);
   auto t0 = pin->GetOrAddReal("problem/visc", "t0", 0.5);
   auto nu_iso = pin->GetReal("diffusion", "mom_diff_coeff_code");

tst/regression/CMakeLists.txt

@@ -49,6 +49,9 @@ setup_test_both("aniso_therm_cond_ring_multid" "--driver ${PROJECT_BINARY_DIR}/b
 setup_test_both("aniso_therm_cond_gauss_conv" "--driver ${PROJECT_BINARY_DIR}/bin/athenaPK \
   --driver_input ${PROJECT_SOURCE_DIR}/inputs/diffusion.in --num_steps 24" "convergence")
 
+setup_test_both("viscosity" "--driver ${PROJECT_BINARY_DIR}/bin/athenaPK \
+  --driver_input ${PROJECT_SOURCE_DIR}/inputs/viscosity.in --num_steps 6" "convergence")
+
 setup_test_both("field_loop" "--driver ${PROJECT_BINARY_DIR}/bin/athenaPK \
   --driver_input ${PROJECT_SOURCE_DIR}/inputs/field_loop.in --num_steps 12" "convergence")
 

tst/regression/test_suites/viscosity/viscosity.py

@@ -0,0 +1,166 @@
+# ========================================================================================
+# AthenaPK - a performance portable block structured AMR MHD code
+# Copyright (c) 2023, Athena Parthenon Collaboration. All rights reserved.
+# Licensed under the 3-clause BSD License, see LICENSE file for details
+# ========================================================================================
+
+# Modules
+import math
+import numpy as np
+import matplotlib
+
+matplotlib.use("agg")
+import matplotlib.pylab as plt
+import sys
+import os
+import itertools
+import utils.test_case
+from scipy.optimize import curve_fit
+
+# To prevent littering up imported folders with .pyc files or __pycache_ folder
+sys.dont_write_bytecode = True
+
+int_cfgs = ["unsplit", "rkl2"]
+res_cfgs = [256, 512, 1024]
+tlim = 2.0
+nu = 0.25
+
+all_cfgs = list(itertools.product(res_cfgs, int_cfgs))
+
+
+def get_outname(all_cfg):
+    res, int_cfg = all_cfg
+    return f"{res}_{int_cfg}"
+
+
+class TestCase(utils.test_case.TestCaseAbs):
+    def Prepare(self, parameters, step):
+        assert parameters.num_ranks <= 4, "Use <= 4 ranks for diffusion test."
+
+        res, int_cfg = all_cfgs[step - 1]
+
+        outname = get_outname(all_cfgs[step - 1])
+
+        parameters.driver_cmd_line_args = [
+            "parthenon/mesh/nx1=%d" % res,
+            "parthenon/meshblock/nx1=64",
+            "parthenon/mesh/x1min=-6.0",
+            "parthenon/mesh/x1max=6.0",
+            "parthenon/mesh/nx2=1",
+            "parthenon/meshblock/nx2=1",
+            "parthenon/mesh/x2min=-1.0",
+            "parthenon/mesh/x2max=1.0",
+            "parthenon/mesh/nx3=1",
+            "parthenon/meshblock/nx3=1",
+            "parthenon/output0/id=%s" % outname,
+            "parthenon/time/tlim=%f" % tlim,
+            "diffusion/mom_diff_coeff_code=0.25",
+            "diffusion/integrator=%s" % int_cfg,
+        ]
+
+        return parameters
+
+    def Analyse(self, parameters):
+        sys.path.insert(
+            1,
+            parameters.parthenon_path
+            + "/scripts/python/packages/parthenon_tools/parthenon_tools",
+        )
+
+        try:
+            import phdf
+        except ModuleNotFoundError:
+            print("Couldn't find module to read Parthenon hdf5 files.")
+            return False
+
+        tests_passed = True
+
+        def get_ref(x):
+            return (
+                1e-6
+                / np.sqrt(4.0 * np.pi * nu * (0.5 + tlim))
+                * np.exp(-(x**2.0) / (4.0 * nu * (0.5 + tlim)))
+            )
+
+        num_rows = len(res_cfgs)
+        num_cols = len(int_cfgs)
+        fig, p = plt.subplots(num_rows + 1, 2, sharey="row", sharex="row")
+
+        l1_err = np.zeros((len(int_cfgs), len(res_cfgs)))
+        for step in range(len(all_cfgs)):
+            outname = get_outname(all_cfgs[step])
+            data_filename = f"{parameters.output_path}/parthenon.{outname}.final.phdf"
+            data_file = phdf.phdf(data_filename)
+            prim = data_file.Get("prim")
+            zz, yy, xx = data_file.GetVolumeLocations()
+            mask = yy == yy[0]
+            v2 = prim[2][mask]
+            x = xx[mask]
+            res, int_cfg = all_cfgs[step]
+            row = res_cfgs.index(res)
+            col = int_cfgs.index(int_cfg)
+
+            v2_ref = get_ref(x)
+            l1 = np.average(np.abs(v2 - v2_ref))
+            l1_err[
+                int_cfgs.index(int_cfg),
+                res_cfgs.index(res),
+            ] = l1
+            p[row, col].plot(x, v2, label=f"N={res} L$_1$={l1:.2g}")
+
+        # Plot convergence
+        for j, int_cfg in enumerate(int_cfgs):
+            p[0, j].set_title(f"Integrator: {int_cfg}")
+
+            p[-1, j].plot(
+                res_cfgs,
+                l1_err[j, :],
+                label=f"data",
+            )
+
+            # Simple convergence estimator
+            conv_model = lambda log_n, log_a, conv_rate: conv_rate * log_n + log_a
+            popt, pconv = curve_fit(conv_model, np.log(res_cfgs), np.log(l1_err[j, :]))
+            conv_a, conv_measured = popt
+            # Note that the RKL2 convergence on the plots is currently significantly better
+            # than expected (<-3) though the L1 errors themself are larger than the unsplit
+            # integrator (as expected).
+            # For a more reasonable test (which would take longer), reduce the RKL2 ratio to,
+            # say, 200 and extend the resolution grid to 1024 (as the first data point at N=128
+            # is comparatively worse than at N>128).
+            if conv_measured > -1.98:
+                print(
+                    f"!!!\nConvergence for test with {int_cfg} integrator "
+                    f"is worse ({conv_measured}) than expected (-1.98).\n!!!"
+                )
+                tests_passed = False
+            p[-1, j].plot(
+                res_cfgs,
+                np.exp(conv_a) * res_cfgs**conv_measured,
+                ":",
+                lw=0.75,
+                label=f"Measured conv: {conv_measured:.2f}",
+            )
+
+        p[-1, 0].set_xscale("log")
+        p[-1, 0].set_yscale("log")
+        p[-1, 0].legend(fontsize=6)
+        p[-1, 1].legend(fontsize=6)
+
+        # Plot reference lines
+        x = np.linspace(-6, 6, 400)
+        for i in range(num_rows):
+            for j in range(num_cols):
+                y = get_ref(x)
+                p[i, j].plot(x, y, "-", lw=0.5, color="black", alpha=0.8)
+                p[i, j].grid()
+                p[i, j].legend(fontsize=6)
+
+        fig.tight_layout()
+        fig.savefig(
+            os.path.join(parameters.output_path, "visc.png"),
+            bbox_inches="tight",
+            dpi=300,
+        )
+
+        return tests_passed