Research On Numerical Methods For Two Types Of MGD Equations

The main purpose of this paper is to study numerical methods for two types of MGD equations. The first type is magnetogasdynamic flow system; The second type is non-ideal isentropic magnetogasdynamics with a transverse magnetic field. These two types of equations have a wide range of applications in astrophysics, energy science and plasma physics. The main work of this paper includes the following aspects:1. For two types of magnetogasdynamic equations, achieved Roe, HLLC scheme to solve these two types of one-dimensional equations. For magnetogasdynamic flow system, according to the three conditions of Roe matrix, a Roe matrix is obtained without any hypothesis on the specific heat ratio. And when it is reduced to the Euler equations, a new average Roe average for Euler equation is obtained. As to non-ideal isentropic magnetogasdynamics, provided two different ways to construct Roe matrix, one is following the idea of the literature[1]and the other is based on the direct method, the same Roe matrix is obtained by the two methods. For HLLC scheme, according to the idea of constructing HLLC scheme for gas dynamics and characteristics of two types of equations, the HLLC schemes for two types of equations are constructed. And then compared several schemes, analyze the numerical results and verify the validity of the schemes.2. Constructed a class of symmetric predictor-corrector TVD scheme based on a class of upwind predictor-corrector TVD scheme, and theoretical analysis is given,and compared it with the symmetric predictor-corrector TVD scheme and two-step component-wise TVD scheme. It indicates that symmetric predictor-corrector TVD scheme has better shock-capture ability than other schemes.3. Achieved a RKDG method based on several limiters for the problems herein considered, and a careful analysis of the advantages and disadvantages of various types of limiter, concluded that the use of SlopeLimitN limiter has better shockcapture ability, which helped us choose limiter.4. A new class of WENO-NIP-type schemes is presented based on Newton interpolation polynomial. For this type of schemes, in the L1 and L2sense, respectively, WENO-NIP-L1 scheme and WENO-NIP-L2 scheme are obtained, and compare them with the classical WENO-JS scheme and WENO-Z scheme, for WENONIP-L2 scheme, it provides at least similar or improved behaviors over the WENO-Z scheme. Compared with WENO-Z and WENO-NIP-L2 scheme, the WENO-NIP-L1 scheme is more high-resolution. And the form of smoothness indicators are more clarity and the works for evaluating the explicit form of smoothness indicator is less when considering higher than fifth-order schemes.