Combining Molecular Dynamics Rkdg Finite Element Methods In Fluid Mechanics

In this work, we detailedly introduced the whole ideas of RKDG finite element method and the theory of constructing gas-kinetic schemes based on Boltzmann equation. And then presented a kind of new computational method for solving Id and 2d compressible Euler equations, i.e. firstly, we discretize Euler equations in the space with discontinuous Galerkin finite element method; secondly, we discretize temporal variable t with Runge-Kutta formula; thirdly, for numerical fluxes constructing, we give two kinds of different numerical fluxes-KFVS and BGK numerical fluxes by using gas-kinetic schemes. The new schemes hold the main advantages of the DG finite element method: the method can easily handle complicated geometries and the boundary conditions; the method is highly parallelizable. Moreover, with gas-kinetic schemes, the new schemes avoid a computation of Riemann Problem in the element boundary. The disadvantage of the new schemes is the large computational capacity.With the above-mentioned two schemes, we compute a large number of numerical experiments to support our numerical results.