A Meshless MQ-RBF Approach with Artificial Viscosity for Shock-Resolved Shallow Water Flow Simulation

Abstract

In this study, we introduce a meshless computational framework for simulating shallow water flows with shock phenomena using multiquadric radial basis functions (MQ-RBFs). The method approximates spatial derivatives through global collocation without relying on traditional mesh generation. To enhance stability and accurately resolve discontinuities such as hydraulic jumps and oblique shock waves, an artificial viscosity term is incorporated into the momentum equations. Time integration is performed using a second-order Runge-Kutta scheme, offering a balance between accuracy and computational efficiency. The model is validated through several benchmark test cases commonly encountered in hydraulic modeling. Results demonstrate strong agreement with analytical, experimental, and numerical reference solutions, highlighting the method’s robustness and precision in capturing complex flow behavior.