A Class of Hybrid DG/FV Methods for Conservation Laws III: Two-Dimensional Euler Equations (Communications in Computational Physics, 2012)
A concept of "static reconstruction" and "dynamic reconstruction" was introduced for higher-order (third-order or more) numerical methods in our previouswork. Based on this concept, a class of hybrid DG/FV methods had been developedfor one-dimensional conservation law using a "hybrid reconstruction" approach, andextended to two-dimensional scalar equations on triangular and Cartesian/triangularhybrid grids. In the hybrid DG/FV schemes, the lower-order derivatives of the piecewise polynomial are computed locally in a cell by the traditional DG method (calledas "dynamic reconstruction"), while the higher-order derivatives are reconstructed bythe "static reconstruction" of the FV method, using the known lower-order derivativesin the cell itself and in its adjacent neighboring cells. In this paper, the hybrid DG/FVschemes are extended to two-dimensional Euler equations on triangular and Cartesian/triangular hybrid grids. Some typical test cases are presented to demonstratethe performance of the hybrid DG/FV methods, including the standard vortex evolution problem with exact solution, isentropic vortex/weak shock wave interaction,subsonic flows past a circular cylinder and a three-element airfoil (30P30N), transonicflow past a NACA0012 airfoil. The accuracy study shows that the hybrid DG/FVmethod achieves the desired third-order accuracy, and the applications demonstratethat they can capture the flow structure accurately, and can reduce the CPU time andmemory requirement greatly than the traditional DG method with the same order ofaccuracy.