in recent years, the number of research works devoted to applying the highly accurate numerical schemes, in particular compact finite difference schemes, to numerical simulation of complex flow fields with multi-scale structures, is increasing. the use of compact finite-difference schemes are the simple and powerful ways to reach the objectives of high accuracy and low computational cost. compa...

This paper is concerned with the numerical solutions of a variable-order space-time fractional reaction-diffusion model. The space-time fractional derivative is considered in the sense of Riesz-Feller, the system is defined by replacing the second order space derivatives with the variable Riesz-Feller derivatives. The problem is solved by an explicit finite difference method. Finally, simulatio...

The present work is dedicated to the study of numerical schemes for a viscoelastic bar vibrating longitudinally and having its motion limited by rigid obstacles at the both ends. Finite elements and finite difference schemes are presented and their convergence is proved. Finally, some numerical examples are reported and analyzed.

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equation...

In this paper we study numerically the KdV-top equation and compare it with the Boussinesq equations over uneven bottom. We use here a finite-difference scheme that conserves a discrete energy for the fully discrete scheme. We also compare this approach with the discontinuous Galerkin method. For the equations obtained in the case of stronger nonlinearities and related to the Camassa-Holm equat...

This paper develops a semi-analytic technique for generating smooth nonuniform grids for the numerical solution of singularly perturbed two-point boundary value problems. It is based on the usual idea of mapping a uniform grid to the desired nonuniform grid. We introduce the W-grid, which depends on the perturbation parameter 1. For problems on [0,1] with a boundary layer at one end point, the ...

In this paper, we propose a high order residual distribution conservative finite difference scheme for solving convection– diffusion equations on non-smooth Cartesian meshes. WENO (weighted essentially non-oscillatory) integration and linear interpolation for the derivatives are used to compute the numerical fluxes based on the point values of the solution. The objective is to obtain a high ord...

The analysis of the Multi Point Flux Approximation (MPFA) method has so far relied on the possibility of seeing it as a mixed finite element method for which the convergence is then established. This type of analysis has been successfully applied to triangles and quadrilaterals, also in the case of rough meshes. The MPFA method has however much in common with another well known conservative met...

In this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

We study mixed-moment models (full zeroth moment, half higher moments) for a Fokker–Planck equation in one space dimension. Mixed-moment minimum-entropy models are known to overcome the zero net-flux problem of full-moment minimum-entropy Mn models. A realizability theory for these mixed moments of arbitrary order is derived, as well as a new closure, which we refer to as Kershaw closure. They ...