论文标题
三角形网格上的Navier-Stokes方程的两阶段四阶气动CPR方法
A two-stage fourth-order gas-kinetic CPR method for the Navier-Stokes equations on triangular meshes
论文作者
论文摘要
在三角形网格上的Navier-Stokes方程中，开发了一种高效的气体运动方案，具有四阶精度。该方案通过重建框架（CPR）框架与强大的气体通量公式结合了有效的校正程序，该框架既计算通量及其时间来源。通量时间衍生的可用性使得采用有效的两阶段时间离散化以达到四阶时间准确性是直接的。此外，通过气体运动进化模型，无粘性和粘性通量均匀地计算并计算出，而无需对粘性通量进行任何单独的处理。结果，当前方案比传统的显式CPR方法更有效，具有单独的粘性通量处理方法和第四阶runge-kutta方法。此外，强大而准确的子电池有限体积（SCFV）限制过程扩展到了陷入困境的单元格的CPR框架，从而导致了流量不连续性的子电池。数值测试证明了当前方案的高精度，效率和鲁棒性，在从亚音速到超音速速度的各种无关和粘性流量问题中。
A highly efficient gas-kinetic scheme with fourth-order accuracy in both space and time is developed for the Navier-Stokes equations on triangular meshes. The scheme combines an efficient correction procedure via reconstruction (CPR) framework with a robust gas-kinetic flux formula, which computes both the flux and its time-derivative. The availability of the flux time-derivative makes it straightforward to adopt an efficient two-stage temporal discretization to achieve fourth-order time accuracy. In addition, through the gas-kinetic evolution model, the inviscid and viscous fluxes are coupled and computed uniformly without any separate treatment for the viscous fluxes. As a result, the current scheme is more efficient than traditional explicit CPR methods with a separate treatment for viscous fluxes, and a fourth order Runge-Kutta approach. Furthermore, a robust and accurate subcell finite volume (SCFV) limiting procedure is extended to the CPR framework for troubled cells, resulting in subcell resolution of flow discontinuities. Numerical tests demonstrate the high accuracy, efficiency and robustness of the current scheme in a wide range of inviscid and viscous flow problems from subsonic to supersonic speeds.
