| In the field of computational fluid dynamics,the shallow water wave equations have always been a very important mathematical physics model,and a large number of shallow water wave equations are widely used in the exploration of natural science and engineering applications.Benjamin-Bona-Mahoney equation and DegasperisProcesi equation are two types of classical shallow water wave equations.The two types of equations have discontinuous solutions.Benjamin-Bona-Mahoney equation has expansion shock solution,and Degasperis-Procesi equation has shock solution.As an important discrete method for numerically solving partial differential equations,the weighted essential non-oscillation(WENO)method has been paid much attention.It has the advantages of high precision and no oscillation which catch discontinuous solutions accurately.In this paper,the numerical discretizations of two above important shallow water wave equations are studied,and the modified high-order WENO spatial discretization schemes of Benjamin-Bona-Mahoney equation and degasperis-procesi equation are constructed respectively.And the full discretization schemes of the equations are given by combining with the third-order TVD Runge-Kutta time discretization scheme.Finally,numerical examples ars used to test the methods.The experiments show that the methods can guarantee good numerical results of both equations and achieve the expected goal.The main achievements and innovations of this paper are as follows:1?The expansion shock solutions of Benjamin-Bona-Mahoney equation have a strong physical background.In this paper,the high-order WENO format of Benjamin-Bona-Mahoney equation is constructed,and the expansion shock solutions of the equation are simulated.2?Aiming at the traditional WENO format,the non-linear weight allocation method is improved,and the weight of the new method is proved to be closer to the ideal weight in theory,thus making the numerical results more accurate. |
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