粘性机制下一类熵相容格式的对比研究  

Comparative Study on A Class of Entropy-Consistent Schemes Based on Viscosity Mechanism

作　　者：梁楠[1] 封建湖[1] 刘友琼[1] 任炯[1] 

机构地区：[1]长安大学理学院,西安710064

出　　处：《数学的实践与认识》2013年第24期227-236,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11171043);长安大学中央高校基本科研业务费项目(CHD2102TD015)

摘　　要：研究了一种人工和物理耗散机制下的离散熵相容格式,探讨数值粘性和物理粘性的大小以及它们所起的作用.所得结论是:在激波捕捉的过程中,粘性系数越大,则无需加入人工粘性项;粘性系数较小时,除了物理粘性项,还需要加入人工粘性项来得到熵相容格式.首先研究了一维粘性Burgers方程离散熵相容格式,再将其推广至Navier-Stokes方程.数值算例采用空间半离散格式,并结合显式三步三阶Runge-Kutta(RK3)方法进行时间推进.这两类方程的数值结果表明,最终选取的熵相容格式能够准确地捕捉到激波.A class of entropy-consistent fluxes which is obtained by using artificial and phys- ical diffusion mechanisms is developed in order to capture a shock wave accurately. Explore the size and the role of the numerical viscosity and physical viscosty. The new scheme does not need to add artificial viscosity term for larger viscosity, but does need both the artificial viscosity term and physical viscosity term for smaller viscosity. We applied the new scheme to one-dimensional viscous Burgers equation, then to Navier-Stokes equations. For spatial derivatives discretisation, we use the proposed entropy-consistent flux,and the explicit three- stage third-order Runge-Kutta （RK3） method for time evolution. Numerical results show that this new class of entropy-consistent schemes could capture the shocks accurately.

关 键 词：熵相容格式 物理粘性项 Navier—Stokes方程 

分 类 号：O175[理学—数学]