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# MLPG Method Based on Rankine Source Solution for Simulating Nonlinear Water Waves

Q.W. Ma1

School of Engineering and Mathematical Sciences, City University, Northampton Square, London, UK, EC1V 0HB

Computer Modeling in Engineering & Sciences 2005, 9(2), 193-210. https://doi.org/10.3970/cmes.2005.009.193

## Abstract

Recently, the MLPG (Meshless Local Petrov-Galerkin Method) method has been successfully extended to simulating nonlinear water waves [Ma, (2005)]. In that paper, the author employed the Heaviside step function as the test function to formulate the weak form over local sub-domains, acquiring an expression in terms of pressure gradient. In this paper, the solution for Rankine sources is taken as the test function and the local weak form is expressed in term of pressure rather than pressure gradient. Apart from not including pressure gradient, velocity gradient is also eliminated from the weak form. In addition, a semi-analytical technique is developed to estimate the domain integral involved in this method, rendering it unnecessary to evaluate velocities at a quite large number of points. These features potentially make the numerical discretisation of the governing equations relatively easier and more efficient. The method is validated by simulating various water waves generated by a wavemaker and by motions of a tank. Good agreement of results with those from publications is achieved.

## Keywords

APA Style
Ma, Q. (2005). MLPG method based on rankine source solution for simulating nonlinear water waves. Computer Modeling in Engineering & Sciences, 9(2), 193-210. https://doi.org/10.3970/cmes.2005.009.193
Vancouver Style
Ma Q. MLPG method based on rankine source solution for simulating nonlinear water waves. Comput Model Eng Sci. 2005;9(2):193-210 https://doi.org/10.3970/cmes.2005.009.193
IEEE Style
Q. Ma, "MLPG Method Based on Rankine Source Solution for Simulating Nonlinear Water Waves," Comput. Model. Eng. Sci., vol. 9, no. 2, pp. 193-210. 2005. https://doi.org/10.3970/cmes.2005.009.193

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