Relation between diffusive terms and Riemann solver in WCSPH

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10485749" target="_blank" >RIV/00216208:11320/24:10485749 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21220/24:00375804

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=gvjIy7e7sy" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=gvjIy7e7sy</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.camwa.2024.05.016" target="_blank" >10.1016/j.camwa.2024.05.016</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Relation between diffusive terms and Riemann solver in WCSPH

Popis výsledku v původním jazyce

The widely used weakly compressible variant of Smoothed Particle Hydrodynamics (SPH) method suffers from density and hence pressure oscillations. This is due to the particle Lagrangian nature of the SPH method in combination with weakly compressible assumption, explicit time scheme and that the substitutions of the derivatives in the SPH method are central. There are two common strategies how to suppress these issues. One of them is to use numerical diffusive term which is added to the continuity equation in order to suppress the spurious oscillation of density field. The second option is to describe the particle -particle interaction in terms of Riemann problem and use Riemann solver, which provides numerical dissipation, to handle particle interactions. In our work, we deal with the relation between these two approaches. For the constant reconstruction and for the linear reconstruction we show that the usage of Riemann solvers is due to its intrinsic numerical viscosity equivalent to the usage of diffusive terms based on even derivatives, with the difference that the Riemann solvers lead to a significantly higher diffusivity value then the standard diffusive terms. We also discuss the usage of limiters for cases with the linear reconstruction of the solution. Moreover, for both, the constant and the linear reconstruction, we analyze additional terms resulting from the employed Riemann solver also for the momentum equation. Combining these results we obtain equivalent partial differential equations, which are the result of the usage of the Riemann solver.

Název v anglickém jazyce

Relation between diffusive terms and Riemann solver in WCSPH

Popis výsledku anglicky

The widely used weakly compressible variant of Smoothed Particle Hydrodynamics (SPH) method suffers from density and hence pressure oscillations. This is due to the particle Lagrangian nature of the SPH method in combination with weakly compressible assumption, explicit time scheme and that the substitutions of the derivatives in the SPH method are central. There are two common strategies how to suppress these issues. One of them is to use numerical diffusive term which is added to the continuity equation in order to suppress the spurious oscillation of density field. The second option is to describe the particle -particle interaction in terms of Riemann problem and use Riemann solver, which provides numerical dissipation, to handle particle interactions. In our work, we deal with the relation between these two approaches. For the constant reconstruction and for the linear reconstruction we show that the usage of Riemann solvers is due to its intrinsic numerical viscosity equivalent to the usage of diffusive terms based on even derivatives, with the difference that the Riemann solvers lead to a significantly higher diffusivity value then the standard diffusive terms. We also discuss the usage of limiters for cases with the linear reconstruction of the solution. Moreover, for both, the constant and the linear reconstruction, we analyze additional terms resulting from the employed Riemann solver also for the momentum equation. Combining these results we obtain equivalent partial differential equations, which are the result of the usage of the Riemann solver.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computers and Mathematics with Applications

ISSN

0898-1221

e-ISSN

1873-7668

Svazek periodika

167

Číslo periodika v rámci svazku

167

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

10

Strana od-do

239-248

Kód UT WoS článku

001246767700002

EID výsledku v databázi Scopus

2-s2.0-85194075668