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

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).