低耗散TVD格式的构造

目的　为进一步提高双曲型方程数值解的精度，减少数值耗散，同时保证稳定性，处理有强间断的流动问题； 方法　从总变差减小（ＴＶＤ）定义出发，分析保证数值解ＴＶＤ的条件，找出满足研究目的的可能性和途径； 结果　首次提出和证明双曲型方程数值解ＴＶＤ的充分必要条件，并据此简化导出适用于时间显示格式的ＴＶＤ充分条件，并据此构造了一种低耗散ＴＶＤ 格式； 结论　进行的数值实验证明，高分辨格式可以进一步减小数值耗散，提高数值解精度；

Construction of Low Numerical Dissipation TVD Schemes

Aim To reduce the numerical dissipation, increase accuracy of numerical solution of hyperbolic equations, and keep numerical stability, solving the flow problem with contact discontinuity. Methods From the definition of TVD, the general condition was analysed to make numerical solution TVD achieve the goal. Results A sufficient and necessary TVD condition was proposed and proved. Based on simplification of the condition, a sufficient TVD condition for time explicit schemes was proposed. A TVD type scheme with lower dissipation was then constructed. Conclusion The numerical dissipation of high resolution schemes can be reduced further more, and numerical test with the scheme shows higher resolution of contact discontinuity.