三维可压缩 Navier-Stokes 方程的间断Galerkin 有限元方法研究

拓展了二维间断 Galerkin(DG)有限元方法研究，将该数值方法用于三维可压缩欧拉方程和 Navier-Stokes方程的求解。基于六面体网格单元，采用插值方法将物面的四边形面网格单元构造为弯曲面网格单元，更好地表述了真实物面特征；物面边界相邻体网格单元相应构造为高阶体网格单元，其余体网格单元采用八节点六面体单元，以较小的计算代价使网格满足 DG 方法计算需求。通过对三维带 bump 管道内流、圆球绕流以及旋转流线体绕流进行的数值求解，验证了边界弯曲方法的可行性及 DG 方法的高精度特性。此外，由于采用了隐式计算方法，仅需较少的时间步就能迭代收敛。

Discontinuous Galerkin method for 3-D compressible Navier-Stokes equations

A curved-boundary based discontinuous Galerkin (DG)method is developed for solving three-dimensional compressible Euler and N-S equations on hexahedral grids.In this method, the quadrilateral face elements are reconstructed to be curved with polynomial interpolation approach,which is better to represent the real boundary.With high-order volume elements clustering only around the boundary surface,this method is easy to implement and requires a small amount of extra computations.Numerical experiments on a variety of flow problems demonstrate that DG method can obtain high-order accurate solutions on relatively coarse grids with the presented curved boundary representation approach.It is worth noting that with an implicit time integration method,converging solutions can be achieved within several time steps.