解对流-扩散方程的时空守恒元与解元法

Method of Space-time Conservation Element and Solution Element for Solving Convection-diffusion Equation

针对一维对流-扩散方程提出了时空守恒元与解元(CE/SE)法.a-μ格式将物理相关变量和它们的空间导数看成是独立的变量,非粘性a-μ格式是中性稳定的,即没有数值损耗,而它修改的a-ε格式,可通过ε来控制数值损耗.当数值解出现间断,a-ε格式并不能防止间断附近的摆动,而a-ε-α-β格式能有效地弥补这些不足.

A new method, the space-time conservation element and solution element （CE/SE） method for solving one-dimension convection diffusion equation is introduced. In α-μ scheme, the physical variables and their spatial derivatives are treated as independent variables. The inviscid α-μ. scheme is neutrally stable, that is, free from numerical dissipation, while the modified α -ε scheme controls numerical dissipation via ε. When discontinuities are present in a numerical solution, the α -ε scheme fails to suppress numerical wiggles that generally take place near these discontinuities, whereas the α-ε-α-β scheme is able to address this issue.