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...

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...

We introduce two kinds of explicit solutions to the convection-reaction equation, ut + (|u| /q)x = u, u, x ∈ R, t ∈ R , q > 1, and employ them to test properties of various computational schemes. From this test we observe that computed solutions using Lax-Friedrichs, MacCormack and Lax-Wendroff schemes break down in a finite time. On the other hand some other schemes including WENO, NT and Godu...

In this article, the two-phase water hammer theoretical and numerical simulation are provided. A mathematical formulation is presented to describe transient one-dimensional flow of bubbly gas-liquid mixtures without phase change in an horizontal pipe. The features two-fluid model for simulating flows investigated. governing equations were obtained from mass momentum conservation laws combined w...

The nearly analytic discrete method (NADM) is a perturbation method originally proposed by Yang et al. (2003) [26] for acoustic and elastic waves in elastic media. This method is based on a truncated Taylor series expansion and interpolation approximations and it can suppress effectively numerical dispersions caused by the discretizating the wave equations when too-coarse grids are used. In the...

We present a novel implicit scheme for the numerical solution of time-dependent conservation laws. The core idea presented method is to exploit and approximate mixed spatial-temporal derivative that occurs naturally when deriving some second order accurate schemes in time. Such an approach introduced context Lax-Wendroff (or Cauchy-Kowalevski) procedure time not completely replaced by space der...

In this paper, we present a new fourth-order upwinding embedded boundary method (UEBM) over Cartesian grids, originally proposed in the Journal of Computational Physics (190, pp. 159, 2003) as a second-order method for treating material interfaces for Maxwell’s equations. In addition to the idea of the UEBM to evolve solutions at interfaces, we utilize the ghost fluid method to construct finite...

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...