Stable Algorithm Based On Lax-Friedrichs Scheme for Visual Simulation of Shallow Water

  • Bandung Arry Sanjoyo Institut Teknologi Sepuluh Nopember
  • Mochamad Hariadi Institut Teknologi Sepuluh Nopember
  • Mauridhi Hery Purnomo Institut Teknologi Sepuluh Nopember
Keywords: shallow water equations, dam-break flow, Lax-Friedrichs scheme, flow visualization

Abstract

Many game applications require fluid flow visualization of shallow water, especially dam-break flow. A Shallow Water Equation (SWE) is a mathematical model of shallow water flow which can be used to compute the flow depth and velocity.  We propose a stable algorithm for visualization of dam-break flow on flat and flat with bumps topography. We choose Lax-Friedrichs scheme as the numerical method for solving the SWE. Then, we investigate the consistency, stability, and convergence of the scheme. Finally, we transform the strategy into a visualization algorithm of SWE and analyze the complexity. The results of this paper are: 1) the Lax-Friedrichs scheme that is consistent and conditionally stable; furthermore, if the stability condition is satisfied, the scheme is convergent; 2) an algorithm to visualize flow depth and velocity which has complexity O(N) in each time iteration. We have applied the algorithm to flat and flat with bumps topography. According to visualization results, the numerical solution is very close to analytical solution in the case of flat topography. In the case of flat with bumps topography, the algorithm can visualize the dam-break flow and after a long time the numerical solution is very close to the analytical steady-state solution. Hence the proposed visualization algorithm is suitable for game applications containing flat with bumps environments.

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Author Biographies

Mochamad Hariadi, Institut Teknologi Sepuluh Nopember

Informatics & Computer

Mauridhi Hery Purnomo, Institut Teknologi Sepuluh Nopember

Informatics & Computer

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Published
2020-06-02
How to Cite
Arry Sanjoyo, B., Hariadi, M., & Purnomo, M. H. (2020). Stable Algorithm Based On Lax-Friedrichs Scheme for Visual Simulation of Shallow Water. EMITTER International Journal of Engineering Technology, 8(1), 19-34. https://doi.org/10.24003/emitter.v8i1.479
Section
Articles