A numerically robust, parallel-friendly variant of BiCGSTAB for the semi-implicit integration of the viscous term in Smoothed Particle Hydrodynamics

TL;DR

This paper introduces a robust, parallel-friendly variant of BiCGSTAB for semi-implicit viscous term integration in Smoothed Particle Hydrodynamics, improving convergence and scalability for complex fluid simulations.

Contribution

It extends previous semi-implicit viscous integration methods to support more boundary models and develops a more robust, parallel-compatible BiCGSTAB solver for non-symmetric linear systems.

Findings

Improved convergence with more accurate boundary models

Excellent strong scaling in parallel computing environments

Satisfactory weak scaling demonstrated in applications

Abstract

Implicit integration of the viscous term can significantly improve performance in computational fluid dynamics for highly viscous fluids such as lava. We show improvements over our previous proposal for semi-implicit viscous integration in Smoothed Particle Hydrodynamics, extending it to support a wider range of boundary models. Due to the resulting loss of matrix symmetry, a key advancement is a more robust version of the biconjugate gradient stabilized method to solve the linear systems, that is also better suited for parallelization in both shared-memory and distributed-memory systems. The advantages of the new solver are demostrated in applications with both Newtonian and non-Newtonian fluids, covering both the numerical aspect (improved convergence thanks to the possibility to use more accurate boundary model) and the computing aspect (with excellent strong scaling and satisfactory weak scaling).