add a multimode RT problem (#307)

This seems to work with both compressible and compressible_fv4.

Author: zingale

pyro/compressible/problems/inputs.rt_multimode

@@ -0,0 +1,33 @@
+# simple inputs files for the four-corner problem.
+
+[driver]
+max_steps = 10000
+tmax = 3.0
+
+
+[io]
+basename = rt_
+n_out = 100
+
+
+[mesh]
+nx = 64
+ny = 192
+xmax = 1.0
+ymax = 3.0
+
+xlboundary = periodic
+xrboundary = periodic
+
+ylboundary = hse
+yrboundary = hse
+
+
+[rt_multimode]
+amp = 0.25
+nmodes = 12
+
+[compressible]
+grav = -1.0
+
+limiter = 2

pyro/compressible/problems/rt_multimode.py

@@ -0,0 +1,85 @@
+"""A multi-mode Rayleigh-Taylor instability."""
+
+import numpy as np
+
+from pyro.util import msg
+
+DEFAULT_INPUTS = "inputs.rt_multimode"
+
+PROBLEM_PARAMS = {"rt_multimode.dens1": 1.0,
+                  "rt_multimode.dens2": 2.0,
+                  "rt_multimode.amp": 1.0,
+                  "rt_multimode.sigma": 0.1,
+                  "rt_multimode.nmodes": 10,
+                  "rt_multimode.p0": 10.0}
+
+
+def init_data(my_data, rp):
+    """ initialize the rt problem """
+
+    # see the random number generator
+    rng = np.random.default_rng(12345)
+
+    if rp.get_param("driver.verbose"):
+        msg.bold("initializing the rt problem...")
+
+    # get the density, momenta, and energy as separate variables
+    dens = my_data.get_var("density")
+    xmom = my_data.get_var("x-momentum")
+    ymom = my_data.get_var("y-momentum")
+    ener = my_data.get_var("energy")
+
+    gamma = rp.get_param("eos.gamma")
+
+    grav = rp.get_param("compressible.grav")
+
+    dens1 = rp.get_param("rt_multimode.dens1")
+    dens2 = rp.get_param("rt_multimode.dens2")
+    p0 = rp.get_param("rt_multimode.p0")
+    amp = rp.get_param("rt_multimode.amp")
+    sigma = rp.get_param("rt_multimode.sigma")
+    nmodes = rp.get_param("rt_multimode.nmodes")
+
+    # initialize the components, remember, that ener here is
+    # rho*eint + 0.5*rho*v**2, where eint is the specific
+    # internal energy (erg/g)
+    xmom[:, :] = 0.0
+    ymom[:, :] = 0.0
+    dens[:, :] = 0.0
+
+    # set the density to be stratified in the y-direction
+    myg = my_data.grid
+
+    ycenter = 0.5*(myg.ymin + myg.ymax)
+
+    p = myg.scratch_array()
+
+    j = myg.jlo
+    while j <= myg.jhi:
+        if myg.y[j] < ycenter:
+            dens[:, j] = dens1
+            p[:, j] = p0 + dens1*grav*myg.y[j]
+
+        else:
+            dens[:, j] = dens2
+            p[:, j] = p0 + dens1*grav*ycenter + dens2*grav*(myg.y[j] - ycenter)
+
+        j += 1
+
+    # add multiple modes to the vertical velocity
+    L = myg.xmax - myg.xmin
+    for k in range(1, nmodes+1):
+        phase = rng.random() * 2 * np.pi
+        mode_amp = amp * rng.random()
+        ymom[:, :] += (mode_amp * np.cos(2.0 * np.pi * k*myg.x2d / L + phase) *
+                       np.exp(-(myg.y2d - ycenter)**2 / sigma**2))
+    ymom /= nmodes
+    ymom *= dens
+
+    # set the energy (P = cs2*dens)
+    ener[:, :] = p[:, :]/(gamma - 1.0) + \
+        0.5*(xmom[:, :]**2 + ymom[:, :]**2)/dens[:, :]
+
+
+def finalize():
+    """ print out any information to the user at the end of the run """