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首页> 外文期刊>International Journal for Numerical Methods in Fluids >Solving a fully nonlinear highly dispersive Boussinesq model with mesh-less least square-based finite difference method
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Solving a fully nonlinear highly dispersive Boussinesq model with mesh-less least square-based finite difference method

机译：用无网格最小二乘有限差分法求解完全非线性的高度分散的Boussinesq模型

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Combining mesh-less finite difference method and least square approximation, a new numerical model is developed for water wave propagation model in two horizontal dimensions. In the numerical formulation of the method, the approximation of the unknown functions and their derivatives are constructed on a set of nodes in a local circular-shaped region. The Boussinesq equations studied in this paper is a fully nonlinear and highly dispersive model, which is composed of the exact boundary conditions and the truncated series expansion solution of the Laplace equation. The resultant system involves a sparse, unsymmetrical matrix to be solved at each time step of the simulation. Matrix solutions are studied to reduce the computing resource requirements and improve the efficiency and accuracy. The convergence properties of the present numerical method are investigated. Preliminary verifications are given for nonlinear wave shoaling problems; the numerical results agree well with experimental data available in the literature. Copyright (c) 2006 John Wiley & Sons, Ltd.
机译：结合无网格有限差分法和最小二乘逼近，建立了二维水平水波传播模型的数值模型。在该方法的数值表示中，未知函数及其导数的近似值构造在局部圆形区域中的一组节点上。本文研究的Boussinesq方程是一个完全非线性且高度分散的模型，由精确的边界条件和Laplace方程的截断级数展开解组成。生成的系统包含一个稀疏，不对称的矩阵，需要在仿真的每个时间步进行求解。对矩阵解决方案进行了研究，以减少计算资源需求并提高效率和准确性。研究了当前数值方法的收敛性。初步验证了非线性波群问题。数值结果与文献中的实验数据吻合良好。版权所有（c）2006 John Wiley＆Sons，Ltd.

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