An efficient geometric approach to solve the slope limiting problem with the Discontinuous Galerkin method on unstructured triangles

作者：Younes Anis; Fahs Marwan^*; Ackerer Philippe

来源：International Journal for Numerical Methods in Biomedical Engineering, 2010, 26(12): 1824-1835.

DOI：10.1002/cnm.1268

• Discontinuous Galerkin
• slope limiter
• transport
• advection
• minimization

The Discontinuous Galerkin method requires the use of an appropriate slope limiter to avoid unphysical oscillations near sharp fronts. Standard limiters, based on the resolution of a minimization problem with linear constraints, are usually solved using an iterative procedure. In this work, an efficient geometric approach is developed to solve the minimization problem on a general triangular mesh. Accuracy and efficiency of the developed limiter are compared with the iterative approach and to a Minmod-based limiter. The results show that both the iterative and the geometric approaches are more accurate than the Minmod-based limiter. The geometric limiter is shown to be more efficient than the other limiters.

• 出版日期2010-12