双曲型守恒律组的高阶Godunov格式(国外英语资料).docVIP

双曲型守恒律组的高阶Godunov格式(国外英语资料) Higher order Godunov schemes for Hyperbolic Conservation Laws Yan Ding 1. Godunov format Brief The model equations are the hyperbolic conservation laws: (1.1) Among them,. Assuming that the mesh is uniform, mesh width is used. A piecewise constant distribution function is constructed for the unit mean distribution at a given time: When. At each cell boundary, the Riemann problem with the following initial conditions is solved: (1.2) For small and sufficient time steps (satisfying conditions), approximate solutions with similar characteristics can be obtained ,, Thus, the approximate solution in the whole computational region is obtained:,, Put it into (1.1), and on the integral there is: Note that the Riemann problem (1.2) follows the solution of the ray, and hence is a constant, thus obtaining the following Godunov format: Among them (1.3) In Fig.1, one of ten cases to consider when calculating the Godunov flux using the solution of the Riemann problem is given. Fig.1 2., two order Godunov scheme (MUSCL) MUSCL calculates the numerical flux through the following steps to achieve the two order extension of the Godunov scheme. STEP (1): Data Reconstrunction. Different from the Godunov scheme, piecewise constant interpolation is used. In each cell, the piecewise linear function is constructed from the mean of the time, that is, the piecewise linear function (2.1) The proper choice is in the upper slope (slope) vector (difference form), at the two endpoint where the value is: (2.2) Called boundary extrapolated values., it is noted that for the Euler equation (1.1) and the vector with three components, there are actually six boundary extrapolated values. in (2.2) STEP (2): Evolution. In each cell, the boundary extrapolated values given by (2.2) will be pushed in time in the following format: At each cell boundary point, there are now two fluxes, and they are generally different, but this step is only intermediate, and thus does not affect the