A Comprehensive Scheme for Fast Simulation of Burgers’ Equation

Abstract

This paper presents a comprehensive scheme to improve the offline as well as online computational time to simulate Burgers’ Equation. A reduced order approximation of the Full Order Model (FOM) is obtained using Non-Linear Moment Matching (NLMM) scheme. The expensive simulation of the underlying nonlinear Sylvester Partial Differential Equation (PDE) is reduced to a system of nonlinear algebraic equations by proper step-by-step simplifications. This reduces the offline computational cost of generating the orthonormal basis vectors substantially. Discrete Empirical Interpolation (DEIM) is used to further reduce the complexity of the underlying nonlinearity which improves the online computation time in solving the reduced system. Reduced Order Model (ROM) thus derived is compared with Proper Orthogonal Decomposition (POD) for different test inputs.