add some protection against negatives in 4th order (#309)

this now uses a mask when we convert from averages to centers.  If either density or internal
energy become negative, then we flag the mask for that zone.  We then go back and reset all of the flagged zones to the cell averages -- this will drop the method to 2nd order in that zone, but its better than having negative density because of a steep gradient.

pyro/compressible_fv4/fluxes.py

@@ -57,6 +57,21 @@ def fluxes(myd, rp, ivars):
     U_cc[:, :, ivars.iymom] = myd.to_centers("y-momentum")
     U_cc[:, :, ivars.iener] = myd.to_centers("energy")
 
+    # the mask will be 1 in any zone where the density or energy
+    # is unphysical do to the conversion from averages to centers
+
+    rhoe = U_cc[..., ivars.iener] - 0.5 * (U_cc[..., ivars.ixmom]**2 +
+                                           U_cc[..., ivars.iymom]**2) / U_cc[..., ivars.idens]
+
+    mask = myg.scratch_array(dtype=np.uint8)
+    mask[:, :] = np.where(np.logical_or(U_cc[:, :, ivars.idens] < 0, rhoe < 0),
+                          1, 0)
+
+    U_cc[..., ivars.idens] = np.where(mask == 1, U_avg[..., ivars.idens], U_cc[..., ivars.idens])
+    U_cc[..., ivars.ixmom] = np.where(mask == 1, U_avg[..., ivars.ixmom], U_cc[..., ivars.ixmom])
+    U_cc[..., ivars.iymom] = np.where(mask == 1, U_avg[..., ivars.iymom], U_cc[..., ivars.iymom])
+    U_cc[..., ivars.iener] = np.where(mask == 1, U_avg[..., ivars.iener], U_cc[..., ivars.iener])
+
     # compute the primitive variables of both the cell-center and averages
     q_bar = comp.cons_to_prim(U_avg, gamma, ivars, myd.grid)
     q_cc = comp.cons_to_prim(U_cc, gamma, ivars, myd.grid)
@@ -66,6 +81,15 @@ def fluxes(myd, rp, ivars):
     for n in range(ivars.nq):
         q_avg.v(n=n, buf=3)[:, :] = q_cc.v(n=n, buf=3) + myg.dx**2/24.0 * q_bar.lap(n=n, buf=3)
 
+    # enforce positivity
+    q_avg.v(n=ivars.irho, buf=3)[:, :] = np.where(q_avg.v(n=ivars.irho, buf=3) > 0,
+                                                  q_avg.v(n=ivars.irho, buf=3),
+                                                  q_cc.v(n=ivars.irho, buf=3))
+
+    q_avg.v(n=ivars.ip, buf=3)[:, :] = np.where(q_avg.v(n=ivars.ip, buf=3) > 0,
+                                                q_avg.v(n=ivars.ip, buf=3),
+                                                q_cc.v(n=ivars.ip, buf=3))
+
     # flattening -- there is a single flattening coefficient (xi) for all directions
     use_flattening = rp.get_param("compressible.use_flattening")
 

pyro/mesh/fv.py

@@ -3,6 +3,8 @@
 
 """
 
+import numpy as np
+
 from pyro.mesh.patch import CellCenterData2d
 
 
@@ -13,14 +15,18 @@ class FV2d(CellCenterData2d):
 
     """
 
-    def to_centers(self, name):
+    def to_centers(self, name, is_positive=False):
         """ convert variable name from an average to cell-centers """
 
         a = self.get_var(name)
         c = self.grid.scratch_array()
         ng = self.grid.ng
         c[:, :] = a[:, :]
         c.v(buf=ng-1)[:, :] = a.v(buf=ng-1) - self.grid.dx**2*a.lap(buf=ng-1)/24.0
+
+        if is_positive:
+            c.v(buf=ng-1)[:, :] = np.where(c.v(buf=ng-1) >= 0.0, c.v(buf=ng-1), a.v(buf=ng-1))
+
         return c
 
     def from_centers(self, name):

pyro/mesh/patch.py

@@ -146,15 +146,15 @@ def __init__(self, nx, ny, *, ng=1,
         self.xr2d = ArrayIndexer(d=xr2d, grid=self)
         self.yr2d = ArrayIndexer(d=yr2d, grid=self)
 
-    def scratch_array(self, *, nvar=1):
+    def scratch_array(self, *, nvar=1, dtype=np.float64):
         """
         return a standard numpy array dimensioned to have the size
         and number of ghostcells as the parent grid
         """
         if nvar == 1:
-            _tmp = np.zeros((self.qx, self.qy), dtype=np.float64)
+            _tmp = np.zeros((self.qx, self.qy), dtype=dtype)
         else:
-            _tmp = np.zeros((self.qx, self.qy, nvar), dtype=np.float64)
+            _tmp = np.zeros((self.qx, self.qy, nvar), dtype=dtype)
         return ArrayIndexer(d=_tmp, grid=self)
 
     def coarse_like(self, N):