Self-adjusting steepness based remapping: A preliminary study

Nonlinear limiters are used to obtain the non-oscillation property in the process of remapping physical quantities (mapping the physical quantities from the old grid to the new grid), which is an important step in the single/multimaterial arbitrary Lagrangian–Eulerian method. However, this operation introduces large numerical dissipation, causing severely smeared physical discontinuities and distortion of the physical quantities. Therefore, the design of an effective limiter that has less numerical dissipation and preserves the sharpness of discontinuous solutions is an area of interest. In this article, we apply the steepness-adjustable harmonic (SAH) limiter (containing a steepness parameter) to the overlay-intersection-based remapping trying to obtain this goal. First, we analyze the construction process of the Barth–Jespersen (BJ) limiter and find a general methodology to modify it with different functions with symmetry property in the existing total-variation-diminishing limiters. Second, we investigate the possibility of other functions that do not possess the symmetry property and find an approximate technique to utilize the SAH limiter (which also does not possess the symmetry property) in the general methodology. Third, we propose a multidimensional method to adaptively calculate the steepness parameter of a whole mesh cell. With these steps, we propose a self-adjusting steepness-based limiter, which is further applied to the over-intersection-based remapping framework. The limiter is then verified by several remapping tests. The numerical results demonstrate a significant improvement in the resolution of discontinuities and the preservation of nominal second-order accuracy for smooth structures. However, the bound-preserving property is inevitably broken owing to the asymmetry of the SAH limiter, and additional techniques should be used to enforce the bounds of the algorithm.