WENO scheme on curvilinear coordinates

selig5576 · July 16, 2019, 09:57

I've been developing a curvilinear FVM code. So far I've implemented the PPM scheme and am looking into adding WENO schemes. So far I've been discretizing the grid metrics using a second-order central.

For the WENO scheme will I need to use a higher-order scheme (5th order?) for the grid metrics. When I use the WENO scheme in curvilinear coordinates I get numerical oscillations, which makes me believe it has to do with the grid metrics. I've implemented the WENO scheme on a purely cartesian grid to verify the implementation was done right.

selig5576 · July 17, 2019, 12:46

Bump. Any ideas?

Eifoehn4 · July 17, 2019, 16:09

Generally linear metrics should be sufficient for high order methods even on fully unstructured meshes. This may not hold for cases including boundary conditions, e.g. walls.

But i am no expert for WENO methods, i only can state that this holds for DG methods.

selig5576 · July 17, 2019, 16:45

That seems reasonable. I will try doing a high-order accurate discretization for the grid metrics.

Random question: Can one formulate a curvilinear transformation for DG methods similar to structured methods (such as FDM and FVM?) Or are your options structured (Cartesian) or unstructured (quads, triangles ,tets, etc)meshes.

Eifoehn4 · July 18, 2019, 02:49

DG methods are not limited to linear meshes. Curved meshes are easy to implement.

July 16, 2019, 09:57	WENO scheme on curvilinear coordinates	#1
selig5576 Senior Member Selig Join Date: Jul 2016 Posts: 213 Rep Power: 10	I've been developing a curvilinear FVM code. So far I've implemented the PPM scheme and am looking into adding WENO schemes. So far I've been discretizing the grid metrics using a second-order central. For the WENO scheme will I need to use a higher-order scheme (5th order?) for the grid metrics. When I use the WENO scheme in curvilinear coordinates I get numerical oscillations, which makes me believe it has to do with the grid metrics. I've implemented the WENO scheme on a purely cartesian grid to verify the implementation was done right.

July 17, 2019, 12:46	Bump	#2
selig5576 Senior Member Selig Join Date: Jul 2016 Posts: 213 Rep Power: 10	Bump. Any ideas?

July 17, 2019, 16:09		#3
Eifoehn4 Senior Member - Join Date: Jul 2012 Location: Germany Posts: 184 Rep Power: 13	Generally linear metrics should be sufficient for high order methods even on fully unstructured meshes. This may not hold for cases including boundary conditions, e.g. walls. But i am no expert for WENO methods, i only can state that this holds for DG methods. __________________ Check out my side project: A multiphysics discontinuous Galerkin framework: Youtube, Gitlab.

July 17, 2019, 16:45	Weno	#4
selig5576 Senior Member Selig Join Date: Jul 2016 Posts: 213 Rep Power: 10	That seems reasonable. I will try doing a high-order accurate discretization for the grid metrics. Random question: Can one formulate a curvilinear transformation for DG methods similar to structured methods (such as FDM and FVM?) Or are your options structured (Cartesian) or unstructured (quads, triangles ,tets, etc)meshes.

July 18, 2019, 02:49		#5
Eifoehn4 Senior Member - Join Date: Jul 2012 Location: Germany Posts: 184 Rep Power: 13	DG methods are not limited to linear meshes. Curved meshes are easy to implement. __________________ Check out my side project: A multiphysics discontinuous Galerkin framework: Youtube, Gitlab.

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