UNIFIED NUMERICAL ANAYSIS BETWEEN THE EXTENDED DARCY'S LAW AND NAVIER-STOKES EQUATION BY USING STABILIZED ISPH METHOD

A comparative study between two numerical solutions of the Navier-Stokes equations

The present study aimed to investigate two numerical solutions of the Navier-Stokes equations. For this purpose, the mentioned flow equations were written in two different formulations, namely (i) velocity-pressure and (ii) vorticity-stream function formulations. Solution algorithms and boundary conditions were presented for both formulations and the efficiency of each formulation was investiga...

A numerical simulation on seepage-induced collapse of caisson breakwater using a stabilized ISPH method

The clarification on the collapse mechanism of a caisson breakwater has been an urgent task in order to reduce damages caused by next millennium tsunamis. In this study, piping destruction of a mound induced by seepage flow is taken into consideration solely. A stabilized ISPH method proposed by Asai (2012) is adopted with some modification associated with the extended Darcy law (Akbari 2013, 2...

Numerical solutions of incompressible Navier–Stokes equations using modi ed Bernoulli’s law

Simulations of incompressible ows are important for many practical applications in aeronautics and beyond, particularly in the high Reynolds number regime. The present formulation is based on Helmholtz velocity decomposition where the velocity is presented as the gradient of a potential plus a rotational component. Substituting in the continuity equation yields a Poisson equation for the potent...

Numerical Methods for the Navier-Stokes equations

On the isentropic compressible Navier-Stokes equation

In this article, we consider the compressible Navier-Stokes equation with density dependent viscosity coefficients. We focus on the case where those coefficients vanish on vacuum. We prove the stability of weak solutions for periodic domain Ω = T as well as the whole space Ω = R , when N = 2 and N = 3. The pressure is given by p = ρ , and our result holds for any γ > 1. In particular, we prove ...