An FCT finite element scheme for ideal MHD equations in 1D and 2D

摘要: Abstract This paper presents an implicit finite element (FE) scheme for solving the equations of ideal magnetohydrodynamics in 1D and 2D. The continuous Galerkin approximation is constrained using a flux-corrected transport (FCT) algorithm. underlying low-order constructed Rusanov-type artificial viscosity operator based on scalar dissipation proportional to fast wave speed. accuracy solution can be improved shock detector which makes it possible prelimit added monotonicity-preserving iterative manner. At FCT correction step, changes conserved quantities are limited way guarantees positivity preservation density thermal pressure. Divergence-free magnetic fields extracted projections predictor into staggered spaces forming exact sequences. In 2D case, field projected space Raviart–Thomas elements. Numerical studies standard test problems performed verify ability proposed algorithms enforce relevant constraints applications MHD flows.