Baran Aydın^1,2, Utku Kânoğlu³

CMES-Computer Modeling in Engineering & Sciences, Vol.21, No.2, pp. 149-156, 2007, DOI:10.3970/cmes.2007.021.149

Abstract We developed analytical solutions to the wind set-down and the wind set-down relaxation problems. The response of the ocean to the wind blowing over a long-narrow and linearly sloping shallow basin is referred to as wind set-down. The shoreline exhibits oscillatory behavior when the wind calms down and the resulting problem is referred to as wind set-down relaxation. We use an existing hodograph-type transformation that was introduced to solve the nonlinear shallow-water wave equations analytically for long wave propagation and obtain an explicit-transform analytical solution for wind set-down. For the wind set-down relaxation, the nonlinear More >

H. Lin, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 117-142, 2001, DOI:10.3970/cmes.2001.002.117

Abstract The truly Meshless Local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations. The local weak form is modified in a very careful way so as to ovecome the so-called Babus^~ka-Brezzi conditions. In addition, The upwinding scheme as developed in Lin and Atluri (2000a) and Lin and Atluri (2000b) is used to stabilize the convection operator in the streamline direction. Numerical results for benchmark problems show that the MLPG method is very promising to solve the convection dominated fluid mechanics problems. More >

H. Lin, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.1, No.2, pp. 45-60, 2000, DOI:10.3970/cmes.2000.001.205

Abstract Due to the very general nature of the Meshless Local Petrov-Galerkin (MLPG) method, it is very easy and natural to introduce the upwinding concept (even in multi-dimensional cases) in the MLPG method, in order to deal with convection-dominated flows. In this paper, several upwinding schemes are proposed, and applied to solve steady convection-diffusion problems, in one and two dimensions. Even for very high Peclet number flows, the MLPG method, with upwinding, gives very good results. It shows that the MLPG method is very promising to solve the convection-dominated flow problems, and fluid mechanics problems. More >