From d2e3c3a6c83b3548275c90f6cfe31f7c0ca24cb2 Mon Sep 17 00:00:00 2001
From: Michael Kuron <mkuron@icp.uni-stuttgart.de>
Date: Tue, 15 Jun 2021 05:26:28 +0000
Subject: [PATCH] FVM: Choose better stencil for derivative in flux for D3Q27
---
pystencils/fd/derivation.py | 8 +++++--
pystencils/fd/finitevolumes.py | 22 ++++++++++++++++--
pystencils_tests/test_fvm.py | 42 ++++++++++++++++++++++++++++++++++
3 files changed, 68 insertions(+), 4 deletions(-)
diff --git a/pystencils/fd/derivation.py b/pystencils/fd/derivation.py
index 868a6872e..e945d7610 100644
--- a/pystencils/fd/derivation.py
+++ b/pystencils/fd/derivation.py
@@ -228,9 +228,10 @@ class FiniteDifferenceStaggeredStencilDerivation:
neighbor: the neighbor direction string or vector at whose staggered position to calculate the derivative
dim: how many dimensions (2 or 3)
derivative: a tuple of directions over which to perform derivatives
+ free_weights_prefix: a string to prefix to free weight symbols. If None, do not return free weights
"""
- def __init__(self, neighbor, dim, derivative=tuple()):
+ def __init__(self, neighbor, dim, derivative=tuple(), free_weights_prefix=None):
if type(neighbor) is str:
neighbor = direction_string_to_offset(neighbor)
if dim == 2:
@@ -281,7 +282,10 @@ class FiniteDifferenceStaggeredStencilDerivation:
# if the weights are underdefined, we can choose the free symbols to find the sparsest stencil
free_weights = set(itertools.chain(*[w.free_symbols for w in weights]))
- if len(free_weights) > 0:
+ if free_weights_prefix is not None:
+ weights = [w.subs({fw: sp.Symbol(f"{free_weights_prefix}_{i}") for i, fw in enumerate(free_weights)})
+ for w in weights]
+ elif len(free_weights) > 0:
zero_counts = defaultdict(list)
for values in itertools.product([-1, -sp.Rational(1, 2), 0, 1, sp.Rational(1, 2)],
repeat=len(free_weights)):
diff --git a/pystencils/fd/finitevolumes.py b/pystencils/fd/finitevolumes.py
index d8f46f394..25992dd8c 100644
--- a/pystencils/fd/finitevolumes.py
+++ b/pystencils/fd/finitevolumes.py
@@ -59,7 +59,10 @@ class FVM1stOrder:
assert ps.FieldType.is_staggered(flux_field)
+ num = 0
+
def discretize(term, neighbor):
+ nonlocal num
if isinstance(term, sp.Matrix):
nw = term.applyfunc(lambda t: discretize(t, neighbor))
return nw
@@ -69,7 +72,9 @@ class FVM1stOrder:
elif isinstance(term, ps.fd.Diff):
access, direction = get_access_and_direction(term)
- fds = FDS(neighbor, access.field.spatial_dimensions, direction)
+ fds = FDS(neighbor, access.field.spatial_dimensions, direction,
+ free_weights_prefix=f'fvm_free_{num}' if sp.Matrix(neighbor).dot(neighbor) > 2 else None)
+ num += 1
return fds.apply(access)
if term.args:
@@ -91,7 +96,20 @@ class FVM1stOrder:
directional_flux = fluxes[0] * int(neighbor[0])
for i in range(1, self.dim):
directional_flux += fluxes[i] * int(neighbor[i])
- discrete_flux = discretize(directional_flux, neighbor)
+ discrete_flux = sp.simplify(discretize(directional_flux, neighbor))
+ free_weights = [s for s in discrete_flux.atoms(sp.Symbol) if s.name.startswith('fvm_free_')]
+
+ if len(free_weights) > 0:
+ discrete_flux = discrete_flux.collect(discrete_flux.atoms(ps.field.Field.Access))
+ access_counts = defaultdict(list)
+ for values in itertools.product([-1, 0, 1],
+ repeat=len(free_weights)):
+ subs = {free_weight: value for free_weight, value in zip(free_weights, values)}
+ simp = discrete_flux.subs(subs)
+ access_count = len(simp.atoms(ps.field.Field.Access))
+ access_counts[access_count].append(simp)
+ best_count = min(access_counts.keys())
+ discrete_flux = sum(access_counts[best_count]) / len(access_counts[best_count])
discrete_fluxes.append(discrete_flux / sp.Matrix(neighbor).norm())
if flux_field.index_dimensions > 1:
diff --git a/pystencils_tests/test_fvm.py b/pystencils_tests/test_fvm.py
index c863c8f45..42127cc76 100644
--- a/pystencils_tests/test_fvm.py
+++ b/pystencils_tests/test_fvm.py
@@ -282,3 +282,45 @@ def test_ek(stencil):
assert a.rhs == b.rhs
# TODO: test source
+
+
+@pytest.mark.parametrize("stencil", ["D2Q5", "D2Q9", "D3Q7", "D3Q19", "D3Q27"])
+@pytest.mark.parametrize("derivative", [0, 1])
+def test_flux_stencil(stencil, derivative):
+ L = (40, ) * int(stencil[1])
+ dh = ps.create_data_handling(L, periodicity=True, default_target='cpu')
+ c = dh.add_array('c', values_per_cell=1)
+ j = dh.add_array('j', values_per_cell=int(stencil[3:]) // 2, field_type=ps.FieldType.STAGGERED_FLUX)
+
+ def Gradient(f):
+ return sp.Matrix([ps.fd.diff(f, i) for i in range(dh.dim)])
+
+ eq = [sp.Matrix([sp.Symbol(f"a_{i}") * c.center for i in range(dh.dim)]), Gradient(c)][derivative]
+ disc = ps.fd.FVM1stOrder(c, flux=eq)
+
+ # check the continuity
+ continuity_assignments = disc.discrete_continuity(j)
+ assert [len(a.rhs.atoms(ps.field.Field.Access)) for a in continuity_assignments] == \
+ [int(stencil[3:])] * len(continuity_assignments)
+
+ # check the flux
+ flux_assignments = disc.discrete_flux(j)
+ assert [len(a.rhs.atoms(ps.field.Field.Access)) for a in flux_assignments] == [2] * len(flux_assignments)
+
+
+@pytest.mark.parametrize("stencil", ["D2Q5", "D2Q9", "D3Q7", "D3Q19", "D3Q27"])
+def test_source_stencil(stencil):
+ L = (40, ) * int(stencil[1])
+ dh = ps.create_data_handling(L, periodicity=True, default_target='cpu')
+ c = dh.add_array('c', values_per_cell=1)
+ j = dh.add_array('j', values_per_cell=int(stencil[3:]) // 2, field_type=ps.FieldType.STAGGERED_FLUX)
+
+ continuity_ref = ps.fd.FVM1stOrder(c).discrete_continuity(j)
+
+ for eq in [c.center] + [ps.fd.diff(c, i) for i in range(dh.dim)]:
+ disc = ps.fd.FVM1stOrder(c, source=eq)
+ diff = sp.simplify(disc.discrete_continuity(j)[0].rhs - continuity_ref[0].rhs)
+ if type(eq) is ps.field.Field.Access:
+ assert len(diff.atoms(ps.field.Field.Access)) == 1
+ else:
+ assert len(diff.atoms(ps.field.Field.Access)) == 2
--
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