An efficient local meshless method for the equal width equation in fluid mechanics

• Published in: Engineering analysis with boundary elements Vol. 131; pp. 258 - 268
• Main Authors: Rasoulizadeh, M.N., Ebadi, M.J., Avazzadeh, Z., Nikan, O.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2021
• Subjects: Equal width equation; Fusion of solitary wave; Local RBF-FD method; Radial basis functions (RBF); Undular bore; Local RBF-FD method; Undular bore; Fusion of solitary wave; Equal width equation; Radial basis functions (RBF)
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/j.enganabound.2021.07.001

This paper proposes an accurate and robust meshless approach for the numerical solution of the nonlinear equal width equation. The numerical technique is applied for approximating the spatial variable derivatives of the model based on the localized radial basis function-finite difference (RBF-FD) method. Another implicit technique based on θ−weighted and finite difference methods is also employed for approximating the time variable derivatives. The stability analysis of the approach is demonstrated by employing the Von Neumann approach. Next, six test problems are solved including single solitary wave, fusion of two solitary waves, fusion of three solitary waves, soliton collision, undular bore, and the Maxwellian initial condition. Then, the L2 and L∞ norm errors for the first example and the I1, I2, and I3 invariants for the other examples are calculated to assess accuracy of the method. Finally, the validity, efficiency and accuracy of the method are compared with those of other techniques in the literature.