Flexible Wedge Product for 0-forms #44
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@lukem12345 has this been subsumed by other PRs? |
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No, in the mean time we have produced wedge products between e.g. primal and dual forms. But methods that perform upwinding have not been implemented. |
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Now that we are doing more fluid stuff, upwinding seems really helpful. I've labeled this good first issue to get over the finish line. |
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Now that we have a general approach to directional derivatives (using Lie(x,y) as our version of d/dx y), could we use that to do upwinding? We specify a vector field x to be the direction in which we define as "upwind" and then reweight operators like wedge or lie derivatives by scalar multiplication by weights? |
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Certainly the 1 dimensional case will be easy to implement and test as a preliminary PR. |
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This PR adds an option for different wedge product weighting schemes.
This implementation is based on Griebel et. al 2017 (Upwind Schemes for Scalar Advection-Dominated Problems in the Discrete Exterior Calculus). Through this, we can reproduce several techniques currently used in finite element/finite volume/finite difference methods, like central differences and upwinding.