Negative flux fixups using positivity-preserving limiters for SN-discontinuous finite element scheme of neutron transport equation on unstructured triangular meshes

Abstract

One significant challenge of spatial discretization for the S_N transport equation is the appearance of negative solutions, resulting in numerical algorithms to be unstable or slow iterative convergence in some problems. The discontinuous Galerkin finite element (DGFEM) spatial scheme on unstructured meshes has attracted much attention in recent years, but the issue of negative solutions is still a long-standing problem. This paper studies a negative flux fixup method using positivity-preserving limiters for solving the S_N-DGFEM neutron transport equation. This method uses the hierarchical basis functions and triangular reference elements to obtain arbitrary high order DGFEM scheme. In the element where appears negativities, a scaling or a rotation positivity-preserving limiter is used to scale or rotate the polynomial distribution to ensure positive solutions. Five different types of problems are selected to verify the accuracy and convergence of the method. Numerical results demonstrate that the method can produce non-negative solutions and maintain the convergence order of the original scheme, as well as not introduce too much additional computational effort.