基于牛顿插值的高分辨率有限体积格式

A High-Resolution Finite Volume Scheme Based on Newtonian Interpolation

有限体积方法在计算流体和热传导的数值计算中占据重要的地位。在数值格式构造的过程中,如何消除对流扩散方程选取间断波为初始条件时数值解所产生的非物理震荡,是有限体积方法主要的研究内容。本文基于对流有界准则(CBC)原理,通过Newton插值多项式的方法构造新的高分辨率有限体积格式。经典算例表明,本文构造的数值格式对于大梯度或间断解有较好的分辨率和数值稳定性。

Finite volume method plays an important role in fluid flow and heat transfer numerical calculation. How to eliminate unphysical oscillations caused by numerical solution of convection diffusion equation selecting discontinuity wave as the initial condition is a key task for studying finite volume method. New high-resolution schemes were constructed by Newton interpolation polynomial based on convection boundness criterion (CBC). Classic test cases demonstrated that the present numerical scheme possesses high resolution and good stability for high gradient and discontinuous solution.