A hybrid algorithm for the simulation of Burgers’ equation near the inviscid limit

Resumo

In this article, a hybrid algorithm has been proposed to solve numerically one dimensional homogeneous Burgers’ equation when the viscosity approaches zero i.e, near inviscid limit. Due to its nonlinear nature, Burgers’ equation describes a variety of phenomena, including turbulence, shock wave and it has numerous applications in the field of heat conduction, gas dynamics, elasticity, etc. The present hybrid scheme is the combination of method of lines, quasilinearisation technique and implicit trapezoidal rule along with the principle of superposition. Firstly, we apply method of lines to reduce the computational procedure and then linearised the non-linear equation using quasilinearisation method and the linearised equation are integrated by using implicit trapezoidal rule with the principle of superposition to obtain the solution. The majority of numerical methods reported in the literature for solving Burger's equation are unable to capture the physical behaviour when viscosity tends to zero. The main objective of the study to develop a hybrid numerical scheme for the simulation of Burger's equation near the inviscid limit. Problems are chosen to validate our results with the existing numerical data and analytical solutions which are found in the literature. Further, the proposed hybrid technique shows better accuracy with the analytical results, more flexible and computationally cost-effective.