Although the focus of the paper is on #SmoothedParticleHydrodynamics, and the simulation of viscous fluids, the key finding is of more general interest: the numerical stability of #BiCGSTAB can be improved by rewriting the standard formulation https://en.wikipedia.org/wiki/Biconjugate_gradient_stabilized_method to avoid catastrophic cancellations in the computation of some important coefficients. Anyone interested in solving large linear systems would benefit from adopting the proposed alternative form of the method.

I'm still preparing my post series on #GPGPU, but in the mean time you can read some about in our most recent published paper:
“A numerically robust, parallel-friendly variant of #BiCGSTAB for the semi-implicit integration of the viscous term in #SmoothedParticleHydrodynamics”, freely accessible for the next 50 days from this link:
https://authors.elsevier.com/a/1fN8C508HsZiG

How does it look like when smoothed particles in a hydrodynamic simulation are doing nothing? Like this.. There is a small amount of initial energy and as you can see, no energy is lost 😆
#SmoothedParticleHydrodynamics #NumericalMethods

For a more hands-on learning experience, the upcoming 16th #SPHERIC International Workshop <https://www.spheric2022.it> offers a #TrainingDay fully dedicated to learning the basics of #SmoothedParticleHydrodynamics, from the theory to practical examples with a #FreeSoftware #OpenSource implementation.

There's a lot to learn, and a lot to research, on #SmoothedParticleHydrodynamics. The #SPHERIC Global Seminars <https://www.spheric-sph.org/global-seminars> cover many interesting aspects of the method and its applications, and are an excellent way to whet your appetite and pique your interest.

The community of researchers and industrial users of #SmoothedParticleHydrodynamics is represented by #SPHERIC, an #ERCOFTAC #SIG with the objective of fostering the development of the method and its adoption <https://spheric-sph.org>.
#SPHERIC defined 5 #GrandChallenges for #SPH:
GC1: #convergence, #consistency and #stability
GC2: #BoundaryConditions
GC3: #adaptivity
GC4: Coupling to other models
GC5: Applicability to #industry

#SmoothedParticleHydrodynamics was originally developed for #astrophysics (modelling star formation), but has expanded to #NavalArchitecture, #OceanEngineering, #waterworks, #aeronautics, #geology, #medicine, just to name a few.
It has caught the attention of several industries, with applications ranging from the design of engines, tires and windshield wipers to the development of wave energy converters, ship-locks, fish-passes and dam spillways.

https://www.youtube.com/watch?v=xqHKa4xJWKw

Let's talk about #SmoothedParticleHydrodynamics (#SPH for short, even though you'll see #sph_ used on other sites, because #SPH also has a very common, very not-safe-for-work meaning …).

Why should we talk about it? Because it's relatively less known than other numerical methods, possibly undeservingly so, and because I love it.

So what is it? SPH is a Lagrangian meshless numerical method primarily used for #ComputationalFluidDynamics (and more recently also #ComputationalMechanics).

#introduction

I work at the Osservatorio Etneo, Catania section of the Italian National Institute for Geophysics and Volcanology #INGV.
Mathematician by formation, scientific software developer by necessity, I work on #lava flow #simulation, #hazard assessment, #risk mitigation.
Much of my work revolves around #ComputationalFluidDynamics (#CFD), w/ a preference for #SmoothedParticleHydrodynamics (#SPH).
I should probably mention my interest in #HPC and #GPGPU, but I ran out of characters …