一类格心型ALE有限体积格式方法

A kind of cell-centered finite volume scheme in arbitrary lagrangian-eulerian method

现在国内外流行的ALE有限体积格式基本上都基于交错网格进行格式的离散。该类格式在进行重映时,速度、密度和能量需要分别进行重映计算,效率较低,而且由于速度在网格角点,而密度、能量在网格中心,重映时会出现动能和内能不协调现象。本文在已有格心型Lagrange有限体积格式研究的基础上,结合Abgrall R.等关于格心型格式下的网格角点速度的计算方法,利用最小二乘法进行高阶插值多项式重构,构造了一类新的格心型的高精度Lagrangian有限体积格式,并结合有效的高精度ENO守恒重映方法,获得了一类格心型的高精度ALE有限体积格式。数值试验的结果说明本文的格式是有效的,高精度的,收敛的,并且避免了物理量的不协调现象。

As we know, most of finite volume schemes in ALE（Arbitrary Lagrangian-Eulerian） method are constructed on the staggered mesh, where the momentum is defined at the nodes and the other variables （density, pressure and specific internal energy） are cell-centered. When remapping of mass and momentum on the staggered mesh, this kind of scheme must use a cell-centered remapping algorithm twice that is very inefficient. Furthermore, there is inconsistent treatment of the kinetic and internal ene A new first order algorithm about computing the velocities at the nodes is introduced by Abgrall rgies. R. et al. In this paper, we reconstruct interpolating polynomials for the values of cell average by using the least square method, and from a new first order algorithm. With a high accurate remapping algorithm, series of numerical experiments are made with our arbitrary Lagrangian-Eulerian method Results show that the method is not only effective, high accurate and convergent, but also remains the consistent treatment of the kinetic and internal energies.