Stable and accurate interface capturing advection schemes
This work addresses the problem of poor accuracy and artifacts in interface capturing for computational fluid dynamics, offering a method that is also suitable for parallel architectures.
The authors developed a stable, low-diffusive interface capturing scheme using multidimensional limiting and appropriate time integration, eliminating geometrical artifacts and achieving artifact-free, instability-free advection. Numerical tests, including the Kothe-Rider case, demonstrated improved accuracy.
In this paper, stable and "low-diffusive" multidimensional interface capturing (IC) schemes using slope limiters are discussed. It is known that direction-by-direction slope-limited MUSCL schemes create geometrical artifacts and thus return a poor accuracy. We here focus on this particular issue and show that the reconstruction of gradient directions are an important factor of accuracy. The use of a multidimensional limiting process (MLP) added with an adequate time integration scheme leads to an artifact-free and instability-free interface capturing (IC) approach. Numerical experiments like the reference Kothe-Rider forward-backward advection case show the accuracy of the approach. We also show that the approach can be extended to the more complex compressible multimaterial hydrodynamics case, with potentially an arbitrary number of fluids. We also believe that this approach is appropriate for multicore/manycore architecture because of its SIMD feature, which may be another asset compared to interface reconstruction approaches.