Abstract
Burgers equation is a fundamental partial differential equation of second order to describe the integrated process of convection-diffusion in physics. It occurs in various areas of applied mathematics and physics, such as modeling of turbulence, boundary layer behavior, shock wave formation, and mass transport. The convective and diffusive terms in Navier-Stokes equation are included in Burgers equation while the pressure term is neglected. A least-square point collocation meshless formula is proposed to discretize the Burgers equation. To verify the present meshless approach, the distributions of velocity for Burgers equation under different Reynolds numbers are investigated. Numerical results show that the proposed approach presents a good simulation of shock wave for Burgers equation with large Reynolds number.
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