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互不混溶相的双曲型及（不完全）抛物型守恒律的仿真环境。以可压缩Navier-Stokes方程（Navier-Stokes Equations, NSE）为例，该方程的解可为诸多重要工程应用提供理论洞察与认知支撑。非线性抛物型方程组的数值模拟极具挑战性，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。针对这类多尺度问题，精准预测需要极高的时空分辨率。我们采用低耗散高分辨率数值方法来捕捉各相内部的动力学行为，相界面的相互作用则通过带有守恒型界面耦合的锐界面水平集方法（sharp-interface level-set method）进行建模，该方法可精准定位界面位置，并能便捷地预设任意耦合条件。为应对由此产生的海量计算负载，我们采用基于块的多分辨率（Multiresolution, MR）算法与自适应局部时间步进方法。通过引入智能标记系统与多分辨率节点内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。我们采用当前前沿编程范式，将这些方法集成至基于C++20的面向对象模块化框架中。此外，我们的实现可高效利用现代高性能计算（High-Performance Computing, HPC）系统中的多级并行性。我们通过模拟多款可压缩多相流问题来验证该框架的性能，问题规模可达O(10^10)个有效自由度（Degrees of Freedom, DOFs）。借助多分辨率技术，我们通常可实现超过90%的内存与计算压缩比。我们通过使用O(10^4)个计算核心进行并行扩展性测试，证明了该框架在各类数值模型下均可实现接近最优的并行性能。