Classical and recent numerical schemes for solving hyperbolic conservation laws were analyzed for computational efficiency and application to nonideal gas flows. The Roe-Pike approximate Riemann solver with entropy correction, the Harten second-order scheme and the extension of the Roe-Pike method to secondorder by the MUSCL strategy were compared for one-dimensional flows of an ideal gas. Thes...

Abstract We perform a comparative accuracy study of the Rusanov, CABARETM, and WENO5 difference schemes used to compute dam break problem for shallow water theory equations. demonstrate that all three have first order convergence inside region occupied by centered rarefaction wave, Rusanov scheme has second in area constant flow between shock while CABARETM there is no local this area. This due...

In the present work we derive and study a non-linear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However, we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite di...

This exploratory work tries to present first results of a novel approach for the numerical approximation of solutions of hyperbolic systems of conservation laws. The objective is to define stable and “reasonably” accurate numerical schemes while being free from any upwind process and from any computation of derivatives or mean Jacobian matrices. That means that we only want to perform flux eval...

The objective of this problem is to study ant foraging lines in one and two dimensions in order to understand their dynamics and examine the fitness of ant colonies. A simple model to describe ant traffic is formulated using conservation laws and a behavioral model. In this work, the behavioral model assumes that the concentration of pheromones is simply proportional to the density of ants. Thi...

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to giv...

Computer simulation of the thermodynamics and dynamics of an intercooled two-stage two-cylinder reciprocating air compressor system is reported and the obtained results discussed. The main emphasis is placed upon modeling the pressure-wave motion in the interconnecting pipework for which the governing equations were solved by means of two different methods: the characteristic mesh method and th...

We propose an investigation of the residual distribution schemes for the numerical approximation of two dimensional hyperbolic systems of conservation laws on general quadrilateral meshes. In comparison to the use of triangular cells, usual basic features are recovered, an extension of the Upwinding concept is given, and a Lax-Wendroff like theorem is adapted for consistency. We show how to ret...

the dynamics of multicomponent adsorption in a fixed bed adsorber is examined numerically. the dynamic model of adsorption in the packed column included axial dispersion and variable space velocity along the bed for the multicomponent adsorption adsorption the pore fluid and the solid phase are in equilibrium with a nonlinear isotherm. the numerical solution is based upon the modified lax-wendr...