The solution of nonlinear Green-Naghdi equation arising in water sciences via a meshless method which combines moving Kriging interpolation shape functions with the weighted essentially non-oscillatory method. (English) Zbl 1524.65452
Summary: In this investigation a new meshless numerical technique is proposed for solving Green-Naghdi equation by combining the moving Kriging interpolation shape functions with the weighted essentially non-oscillatory (WENO) method. The present approach has been taken from [J.-C. Chassaing et al., Comput. Methods Appl. Mech. Eng. 253, 463–478 (2013; Zbl 1297.76110); J. Guo and J.-H. Jung, Appl. Numer. Math. 112, 27–50 (2017; Zbl 1354.65177)]. The convergence order of WENO technique can be studied by the number of interpolation nodes because this method is described by interpolation concept. The proposed method is based on the non-polynomial WENO procedure in order to increase the convergence order and local accuracy. Four examples have been solved that they show the efficiency and accuracy of the proposed method.
MSC:
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35B05 | Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs |
| 65D05 | Numerical interpolation |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
moving Kriging interpolation; weighted essentially non-oscillatory (WENO) method; Green-Naghdi equation; water scienceReferences:
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