Van Leer格式在全速域范围的推广

Extending Van Leer scheme for flows at all speeds

通过对格式耗散项的修正将Van Leer格式推广至全速域流场求解范围。对格式耗散项的分析表明,在低马赫数流动情况下格式耗散项中不应包含声速项,以此为依据对Van Leer迎风分裂格式提出了耗散项的修正方法。结合对控制方程时间导数项的预处理,修正后的格式能够成功地模拟低速流动问题,同时在其他马赫数范围内也不损失格式的收敛性及求解精度。验证算例包括低速、亚、跨及超声速流场,计算结果表明修正后的格式能够有效地用于全速域范围内的流动问题的模拟。

Van Leer scheme was extended for flows at all speeds by modifying its dissipation term.The analysis about the dissipation term shows that the speed of sound should not be contained in this term.Based on this idea,the modification about the dissipation term has been suggested.With time-derivative preconditioning,the modified scheme can simulate the flows at low Mach numbers,and it can preserve the convergence and accuracy in other range of Mach numbers.Numerical experiments,including low speed flow,subsonic flow,transonic flow and supersonic flow,show that the modified scheme can be applied to the flows at all speeds successfully.