Experimental PDE solver in Julia – comparison of flux limiting schemes

نویسندگان

چکیده

Finite Volume Methods (FVM) are high quality methods for solving conservative/hyperbolic partial differential equations (PDEs). A popular class of high-resolution utilize a nonlinear combination low order and via flux limiting functions. Another is the weighted essentially non-oscillatory (WENO) schemes. Here, focus on An experimental finite volume (FV) semi-discrete solver systems hyperbolic PDEs has been implemented in Julia, utilizing Julia’s DifferentialEquations.jl package handling time marching. first upwind formulation used method, central second method. The PDE can be provided either form, or quasi-linear form. In former case, automatic differentiation (AD) ForwardDiff.jl to compute Jacobians vector. Package LinearAlgebra.jl eigenspace Jacobians. implementation allows up 3 internal/external coordinates. More than dozen functions given, with possibility users write their own limiters. user spatial discretization points, source terms PDE. this paper, we will compare various schemes analytic solutions, also simple granulation model (layering). Possible extensions include: (i) higher methods, (ii) more extensive support boundary conditions, (iii) improved terms.

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ژورنال

عنوان ژورنال: Linköping electronic conference proceedings

سال: 2022

ISSN: ['1650-3740', '1650-3686']

DOI: https://doi.org/10.3384/ecp192007