ALPACA - a level-set based sharp-interface multiresolution solver for conservation laws

ALPACA is a simulation environment for simulating hyperbolic and (incompletely) parabolic conservation laws with multiple distinct and immiscible phases. As prominent example, consider the compressible Navier-Stokes equations (NSE). Solutions to these equations give insight and understanding of many important engineering applications. Numerical simulations of nonlinear parabolic systems of equations are very challenging for their complex nonlinear dynamics including the propagations of discontinuities such as shocks and phase interfaces. Accurate predictions require high temporal and spatial resolutions for such multi-scale problems. We utilize low dissipation high-resolution methods to capture the dynamics inside the separate phases. Their interaction is modeled by a sharp-interface level-set method with conservative interface-interaction. This allows to accurately locate the interface position and to easily prescribe arbitrary coupling conditions. We tackle the resulting immense computational loads by using a block-based multiresolution (MR) algorithm and adaptive local time stepping. The level-set treatment is integrated into the MR algorithm with little overhead by employing a smart tagging system and adaptive storage of the fluid data in the MR nodes. We embed these methods in a C++20 object-oriented modular framework using state-of-the-art programming paradigms. Furthermore, our implementation is capable to exploit the multiple levels of parallelism in modern high-performance computing (HPC) systems efficiently. We demonstrate the capabilities of our framework by simulating a variety of compressible multi-phase flow problems. Problem-sizes are of O(10^10) effective degree of freedom (DOFs). By the use of MR, we typically achieve memory and compute compressions of >90%. We demonstrate near-optimal parallel performance for scaling runs using O(10^4) cores, regardless of the employed numerical models.