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.

ALPACA是一款模拟双曲和（不完全）抛物型守恒律的多相不可混溶现象的仿真环境。以压缩性Navier-Stokes方程（NSE）为例，该方程的解为众多重要的工程应用提供了洞察与理解。非线性抛物型方程组的数值模拟因其复杂的非线性动力学特性，如间断的传播，如激波和相界面，而极具挑战性。对于此类多尺度问题，精确预测需要高时间分辨率和空间分辨率。我们采用低耗散的高分辨率方法来捕捉各个相内的动力学。通过采用锐化界面水平集方法与守恒界面交互模型，模拟了这些相之间的相互作用，从而能够精确地定位界面位置，并轻松地设定任意的耦合条件。我们通过使用基于块的多元分辨率（MR）算法和自适应局部时间步长来解决由此产生的巨大计算负载。通过采用智能标记系统和自适应存储MR节点中的流体数据，将水平集处理集成到MR算法中，以实现低开销。我们利用C++20面向对象模块化框架和最先进的编程范式将这些方法嵌入其中。此外，我们的实现能够高效地利用现代高性能计算（HPC）系统中的多级并行性。我们通过模拟各种压缩性多相流问题来展示我们框架的能力。问题规模达到(O(10^{10}))的有效自由度（DOFs）。通过使用MR，我们通常实现大于90%的内存和计算压缩比。我们展示了在O(10^{4})核心上使用近最优并行性能进行扩展运行的能力，无论采用何种数值模型。