TVD finite point method for two-dimensional conservation equation

Abstract

A new meshless method, called total variation diminishing (TVD) finite point method (TVDFP), is proposed. The TVDFP method is developed on the least-square procedure which uses a global stencil of grid points and the two-dimensional (2D) TVD procedure for the approximation of fictitious interface directional fluxes. We present the accuracy of the TVDFP method and several 2D test computations.

Keywords:

• TVD
• meshless method
• two-dimensional conservation equation
• least-square
• interface directional fluxes

2000 AMS Subject Classification :

• 58J45
• 65D25
• 65M12
• 76A02

Acknowledgements

This work was supported by National Natural Science Foundation of China (10701014, 10601009, 10431050), the China Postdoctoral Science Foundation and the Foundation of China Academy of Engineering Physics (2003Z0603).