tristanmontoya / stablespectralelements.jl

StableSpectralElements.jl: Provably stable discontinuous spectral-element methods for conservation laws

StableSpectralElements.jl

StableSpectralElements.jl (formerly CLOUD.jl) is a Julia framework for the numerical solution of hyperbolic and mixed hyperbolic-parabolic conservation laws on general unstructured grids using provably stable discontinuous spectral-element methods of arbitrary order, with an emphasis on dispatched strategies for the evaluation of a broad class of discretization operators. StableSpectralElements.jl supports shared-memory parallelization through multithreading.

Installation

StableSpectralElements.jl is a registered Julia package (compatible with Julia versions 1.8 and above) and can be installed by entering the following commands within the REPL:

using Pkg; Pkg.add("StableSpectralElements")

For further information on the functionality and usage of this package, please refer to the example notebooks as well as the documentation, or feel free to send me an email.

License

This software is released under the GPLv3 license.

stablespectralelements.jl's Issues

Fix calculation of entropy residual (doesn't work for modal schemes)

Reduce compilation time

Code is pretty fast, but compilation time is bad right now, especially in 3D. Possibly due to branches/type inference issues.

Make fluxes like LF dispatch on the two-point flux function and add dissipation to that

Add Euler and Burgers examples

Directional two-point flux

This may improve SIMD'ing as well.

Distributed memory parallelism?

Test flux differencing for curvilinear meshes

Switch to primitive variables before evaluating fluxes

This would make computing the pressure and velocities twice no longer necessary (this wasn't done before #56 was implemented). Maybe some way of storing $\rho V$ and $V$ to compute momentum fluxes a bit faster?

Make flux differencing fully exploit tensor-product structure of operators

Make temporary registers one per thread, not one per element

Test Euler flux-differencing form with sine wave solution to 1D Euler

Implement modal/staggered diagonal-E schemes

Requires simplified version of entropy projection (#62).

Incorrect results for multidimensional advection-diffusion

Investigate using StaticArrays for systems of equations

This is probably faster since the size is known a priori.

Register v0.1.1

@JuliaRegistrator register

Verify accuracy for isentropic vortex (or other smooth Euler flow) problem using standard schemes

Compute error using arbitrary (e.g. over-integrated) quadrature rules

Currently we use the scheme's volume quadrature to evaluate the $L^2$ error. It would be nice if that could be done with higher-order quadrature.

Flux-differencing operator for 1D Burgers' equation

Start with LGL implementation.

Flux-differencing formulations for SBP-Ω/Legendre-Gauss operators

This will require the entropy projection (#62) , and also hybridized operators/correction terms.

Streamline definition of initial conditions/exact solutions

Make error.jl use less memory

Even when the simulation does not run out of memory, the error calculation sometimes does. These are reasonably large 3D meshes, but I don't think error calcs should be the thing that limits how large a problem you can solve.

Optimize conversion to/from entropy variables

Roundoff error seems oddly high ~1e-13 in some cases.

Seems to manifest in conservation error being non-negligible (solution is probably off too, but discretization error masks this). Why we only see this for the 2D Euler equations is a bit of a mystery though, as the results for advection and 1D Euler are fine.

Edit: Removing inverse from metric calculation does not help, so I think it's somewhere in the Euler flux.

Compute numerical flux once per interface

Requires adding additional connectivity fields on top of those in StartUpDG.MeshData

release v0.1.2

@JuliaRegistrator register

Chan-Wilcox conservative-curl metrics

Optimize tensor-product extrapolation operators using BLAS or StaticArrays

This is already done for differentiation and forward/backward transform, but not for the interpolation/extrapolation operator.

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Entropy-conservative numerical fluxes for the Euler equations

I think Ranocha's flux makes most sense since it is KEP and PEP.

Register with updated package name

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Implement entropy projection