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是一款用于模拟含多种不同且不互溶相的双曲（不完全抛物）守恒律的仿真环境。以可压缩Navier-Stokes方程（NSE）为例，该类方程的解可为诸多重要工程应用提供理论洞察与认知理解。非线性抛物型方程组的数值仿真极具挑战，因其蕴含复杂的非线性动力学特性，包括激波与相界面等间断的传播过程。针对这类多尺度问题，精准的数值预测需要极高的时空分辨率。我们采用低耗散高分辨率格式来捕捉各相内部的动力学演化过程，而各相间的相互作用则通过带有守恒型界面交互的锐界面水平集方法进行建模，该方法可精准定位界面位置，且便于预设任意耦合条件。为应对由此产生的巨大计算负载，我们采用基于块的多分辨率（MR）算法与自适应局部时间步进策略。通过引入智能标记系统，并在多分辨率节点内实现流体数据的自适应存储，我们将水平集处理集成至多分辨率算法中，且仅带来极小的性能开销。我们将上述方法集成至基于C++20的面向对象模块化框架中，采用当前前沿的编程范式。此外，本实现可高效利用现代高性能计算（HPC）系统中的多级并行性。我们通过模拟多种可压缩多相流动问题，验证了本框架的性能，所涉及的问题规模可达O(10^10)有效自由度（DOFs）。借助多分辨率技术，我们通常可实现超过90%的内存与计算压缩率。针对采用O(10^4)计算核心的缩放测试运行，无论使用何种数值模型，我们均可实现近最优的并行性能。