ZHENG Supei, WANG Ling, WANG Miaomiao. Solution of 2D Shallow Water Wave Equations With the Moving-Grid Rotating-Invariance Method[J]. Applied Mathematics and Mechanics, 2020, 41(1): 42-53. doi: 10.21656/1000-0887.400124
Citation: ZHENG Supei, WANG Ling, WANG Miaomiao. Solution of 2D Shallow Water Wave Equations With the Moving-Grid Rotating-Invariance Method[J]. Applied Mathematics and Mechanics, 2020, 41(1): 42-53. doi: 10.21656/1000-0887.400124

Solution of 2D Shallow Water Wave Equations With the Moving-Grid Rotating-Invariance Method

doi: 10.21656/1000-0887.400124
Funds:  The National Natural Science Foundation of China(11401045; 11971075)
  • Received Date: 2019-03-26
  • Rev Recd Date: 2019-05-31
  • Publish Date: 2020-01-01
  • In order to improve the resolution of the numerical algorithm for solving the 2D shallow water wave equation, a new algorithm was proposed based on the moving-grid method, with the entropy stable numerical flux function and by means of the mixed numerical flux obtained through the rotating invariance. The numerical solution of the shallow water wave equation and the grid computation process based on the characteristics of the solution were interleaved. The variational principle was used to reconstruct the mesh, and the physical quantity on the new mesh was computed with the 2nd-order precision conservation interpolation formula. The 3rd-order strongly stable Runge-Kutta method and the entropy stable format satisfying the 2nd law of thermodynamics were used to numerically solve the shallow water wave equation. The numerical results show that, the new algorithm has good discontinuity capture ability and high resolution.
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