Developing a Shock-Capturing Formulation with Higher Performance to Capture Normal Standing Shock in All-Speed Regime
Authors
Abstract
The main objective of the present study is to utilize a novel linearization strategy to linearize the convection terms of the quasi-one-dimensional Euler governing equations on collocated grids and to examine its shock-capturing capabilities. To avoid a pressure checkerboard problem on the collocated grids, it is necessary to utilize two velocity definitions at each cell face. Similarly, we define two velocity expressions at cell faces known as convecting and convected velocities. We derive them from the proper combinations of continuity and momentum equations which, in turn, provide a strong coupling among the Euler discretized equations. To achieve this, we utilize an advanced linearization strategy known as Newton-Raphson to linearize the nonlinear convection terms. The key point in this linearization is to preserve the original physics behind the two velocities in the linearization procedure. The performance of the new formulation is then investigated in a converging-diverging nozzle flow. The results show great improvement in both the performance of the original formulation and in capturing shocks. The results also indicate that the new extended formulation is robust enough to be used as an all-speed flow solver.
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