This paper describes the development of a boundary fitted nested grid (BFNG) model to compute tsunami propagation of 2004 Indonesian tsunami in Southern Thailand coastal waters. We develop a numerical model employing the shallow water nested model and an orthogonal boundary fitted grid to investigate the tsunami impact on the Southern Thailand due to the Indonesian tsunami of 2004. Comparisons ...

A new implementation of boundary condition based on the half-covolume and bounce-back rule for the non-equilibrium distribution function for the finite volume LBM is proposed here. The numerical simulation results for the expansion channel flow and driven cavity problem indicate that this method is workable for arbitrary meshes. In addition, the fourth order Runge–Kutta scheme is found to be a ...

In this paper the Wilson nonconforming nite element is considered for solving a class of two-dimensional second-order elliptic boundary value problems. Superconvergence estimates and error expansions are obtained for both uniform and non-uniform rectangular meshes. A new lower bound of the error shows that the usual error estimates are optimal. Finally a discussion on the error behaviour in neg...

Finite difference schemes providing an improved representation of a range of scales (spectral-like resolution) in the evaluation of first, second, and higher order derivatives are presented and compared with well-known schemes. The schemes may be used on non-uniform meshes and a variety of boundary conditions may be imposed. Schemes are also presented for derivatives at mid-cell locations, for ...

We prove several discrete Gagliardo-Nirenberg-Sobolev and Poincaré-Sobolev inequalities for some approximations with arbitrary boundary values on finite volume meshes. The keypoint of our approach is to use the continuous embedding of the space BV (Ω) into L (Ω) for a Lipschitz domain Ω ⊂ R , with N ≥ 2. Finally, we give several applications to discrete duality finite volume (DDFV) schemes whic...

Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e., the aspect ratio AR = ∆y/∆x << 1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce prop...

The collocation method and Galerkin method using parabolic splines are considered. Special adaptive meshes whose number of knots is independent of the small parameter of the problem are used. Unimprovable estimates in the L∞-norm are obtained. For the Galerkin method these estimates are quasioptimal, while for the collocation method they are suboptimal. Introduction It is well known that the sp...