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Picard Iteration Technique for Cross-Sectional Area Calculation in MPS Modeling of Shallow Water Flows

Author(s): Payam Sarkhosh; Peng Wu; Yee-Chung Jin

Linked Author(s): Peng Wu, Yee-chung Jin

Keywords: Shallow water equation; MPS; Particle method; Simulation

Abstract: In the last two decades, mesh-free or particle methods have been widely applied to solve shallow water equations. As the mass conservation is automatically satisfied due to the particle movement with the flow, there is no need to solve the continuity equation under the Lagrangian framework. Accordingly, an algebraic formula is utilized to compute the cross-sectional area using an iterative method. Conventionally, the Newton-Raphson method is adopted in which the convergence may be poor if the initial guess is not close to the solution. The present study introduces a Picard iteration-based framework to solve the density-ratio equation in moving particle simulation (MPS) modeling of cross-sectional averaged shallow water equations. The new strategy results reveal that the iterative convergence is strongly accomplished with the accuracy up to double-machine precision. Furthermore, the Picard method makes it possible to employ a hybrid combination of the gather and scatter interpretations of the density-ratio equation, which promotes the conservation of linear momentum in the proximity of antisymmetric interparticle forces.


Year: 2022

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