Shock computations with adaptive mesh refinement and moving grids

AbstractHighly accurate shock wave problems are presented using a combination of numerical techniques. The new feature of this scheme is the treatment of discontinuities (shocks or contact surfaces) which are replaced by approximate step functions. These approximations permit the solution of the Euler equations within the discontinuity and permits a convenient way of treating source terms within a discontinuity. The strong conservative law form is used throughout.An explicit moving grid technique is used in which a moving frame is found in which the conservation law equations appear stationery in a least squares sense. In this moving frame, it is possible to drastically reduce or eliminate the temporal truncation errors. Thus, the same time integration scheme can be used throughout the computational domain in the discontinuous as well as continuous regions.For accurate physics of wave interactions, a nonlinear Riemann solver is applied. In conjunction with the Riemann solver as new waves from such interactions are created, an adaptive mesh refinement scheme injects new mesh points automatically to define a post collision wave structure.Results are presented for the shock tube problem, the von Neumann spherical blast wave, Noh's spherical shock problem, shock interactions with a set-up and step-down contact discontinuity