中文摘要：

首先构造二维FVWENO（finite volume weighted essentially non-oscillatory）格式：在二维空间模板上构造一个3次多项式.将此模板分割为8个较小的模板,每一个小模板上包含6个单元.在每一个小模板上构造一个2次多项式,要求多项式在单元上的平均值与需重构的物理量在同一单元上的平均值相等.之后,通过计算得到线性权,光滑指示器,非线性权.然后利用TVD Runge-Kutta时间离散方法得到时空一致高阶精度格式.最后,结合两种浸入边界Ghost cell方法,能针对复杂物体流动问题在结构网格上进行正确的数值模拟.

英文摘要：

In this paper,the FVWENO（finite volume weighted essentially non-oscillatory） scheme is proposed on structured meshes.Firstly,we construct a 3-th degree polynomial on the big stencil.Then,we divide the associated stencil into eight smaller stencils which harbor six cells.And we construct different polynomials on different small stencils that match the cell averages of variables on all cells of the same small stencil.After that,we can get the linear weight,the smooth indicator and the nonlinear weight.Then,we use the TVD Runge-Kutta time discrete method to get fully discrete scheme both in space and time.Coupling with the two different immersed boundary Ghost cell methods,we can deal with the complex geometrical body simulations precisely.