不连续性分类
非线性系统
流量(数学)
网格
应用数学
黎曼解算器
黎曼假设
欧拉方程
流体力学
笛卡尔坐标系
间断(语言学)
数学
计算机科学
机械
数学分析
物理
几何学
有限体积法
量子力学
作者
Paul R. Woodward,Phillip Colella
标识
DOI:10.1016/0021-9991(84)90142-6
摘要
Results of an extensive comparison of numerical methods for simulating hydrodynamics are presented and discussed. This study focuses on the simulation of fluid flows with strong shocks in two dimensions. By “strong shocks,” we here refer to shocks in which there is substantial entropy production. For the case of shocks in air, we therefore refer to Mach numbers of three and greater. For flows containing such strong shocks we find that a careful treatment of flow discontinuities is of greatest importance in obtaining accurate numerical results. Three approaches to treating discontinuities in the flow are discussed—artificial viscosity, blending of low- and high-order-accurate fluxes, and the use of nonlinear solutions to Riemann's problem. The advantages and disadvantages of each approach are discussed and illustrated by computed results for three test problems. In this comparison we have focused our attention entirely upon the performance of schemes for differencing the hydrodynamic equations. We have regarded the nature of the grid upon which such differencing schemes are applied as an independent issue outside the scope of this work. Therefore we have restricted our study to the case of uniform, square computational zones in Cartesian coordinates. For simplicity we have further restricted our attention to two-dimensional difference schemes which are built out of symmetrized products of one-dimensional difference operators.
科研通智能强力驱动
Strongly Powered by AbleSci AI