Numerical Solution of Burger's Equation by Undetermined Coefficient Method for Higher Order Scheme

Abstract

Undetermined coefficient method is proposed to derive higher order schemes for solving Burger’s equation. The undetermined coefficient method was proved that some well-known schemes can be derived although their original derivations are different from each other. In this proposed method for solving the 1-D Burger’s equation, stability and accuracy of the new scheme are analyzed by comparing the computed results with exact solutions of one-dimensional pure convection equation. Effectiveness of the proposed method is also analyzed by comparing with the results using other schemes. This scheme was applied to simulate hydraulic jump in one-dimensional flow with different ratios of initial upstream water depth to downstream one. From the obtained results, it shows that this new scheme has the ability to simulate a moving hydraulic jump well.