In the computation of unsteady Euler equations of gas dynamics the development of numerical schemes that can accurately capture a shock irrespective of its strength or grid-inclination has received considerable research-interest in recent times. Towards this goal multidimensional-upwind schemes have gained popularity. However, these schemes are computationally expensive. The class of self-adjusting-hybrid methods is a promising alternative that can produce multidimensional-like effects with a lower computational cost. Choices of the two schemes for hybridization and the shock switch are two crucial issues that affect the performance of a self-adjusting-hybrid scheme. The design of a robust and versatile shock switch is a crucial issue that affects the performance of a hybrid scheme. Shock switches of varied applicability and complexity have been reported in literature. However, most of the existing shock switches suffer from limitations like requirement of a large stencil-size, dependence on too many user-adjustable parameters and susceptibility to activation near smooth extrema. This paper presents the superior performance of a recently-developed shock switch to obtain a simple, yet robust hybrid method that combines the AUSM and DRLLF schemes. The switch works based on the gradient of contravariant Mach number across neighbouring cell-interfaces. The performance-comparison of the Mach-number-gradient-based switch is done with a popular switch proposed by Swanson and Turkel - taken as the representative of switches that are not based on gradients - using a set of one- and two-dimensional inviscid compressible-flow problems. It is demonstrated that the hybrid scheme produces multidimensional-like effects with the gradient-based switch for the wide range of problems. Further, the performance of Swanson and Turkel's switch is improved by tuning a user-adjustable parameter that depends on the local grid-scale. In that context, the superior qualities of the Mach-number-gradient-based switch are established in terms of its versatility, robustness, a small stencil-size and freedom from user-intervention.
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