On the numerical integration of multi-dimensional, initial boundary value problems for the Euler equations in quasi-linear form

Abstract

A matricial formalism to solve multi-dimensional initial boundary values problems for hyperbolic equations written in quasi-linear based on the λ scheme approach is presented. The derivation is carried out for nonorthogonal, moving systems of curvilinear coordinates. A uniform treatment of the integration at the boundaries, when the boundary conditions can be expressed in terms of combinations of time or space derivatives of the primitive variables, is also presented. The methodology is validated against a two-dimensional test case, the supercritical flow through the Hobson cascade n.2, and in three-dimensional test cases such as the supersonic flow about a sphere and the flow through a plug nozzle.

On high-order shock-fitting and front-tracking schemes for numerical simulation of shock–disturbance interactions

“…Moretti used Riemann's characteristic equations, discretizing them based on the direction of propagation of the associated waves. Such methods were named k-schemes [43] and were used exclusively with the shock-fitting method [44][45][46][47][48]. Moretti also considered multi-dimensional flows where shocks are not aligned with any grid lines but float across the grids [49].…”

Three-dimensional boundary conditions for direct and large-eddy simulation of compressible viscous flows

“…As discussed by Valorani and Favini [23], transverse terms on edges and corners are coupled with characteristic waves traveling along directions orthogonal to adjacent boundaries. Therefore, three-dimensional characteristic coupled waves must be considered.…”

Direct Numerical Simulations of Turbulent Flow Interactions with Strong Shocks Using Shock-Fitting Method

“…Moretti used Reimann's characteristic equations; discretizing them based on the direction of propagation of the associated waves. Such methods were named -schemes [44] and were used exclusively with shock-fitting method [45][46][47][48][49]. Moretti also considered multidimensional flows where shocks are not aligned with any grid lines but float across the grids [50].…”