Two Numerical Methods Based On Discretization Of The MPS Method For Solving The Two-dimensional Burgers’ Equation
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The Burgers’ equation is an important and basic nonlinear partial differential equation in fluid dynamics, and has been used as a model equation in other fields, such as modeling of shock waves, gas dynamics, turbulence, and large bubble structures consisting of clusters of galaxies in space. Many researchers have proposed various numerical methods for solving the Burgers’ equation, such as the finite difference method, finite element method, boundary element method, etc. The objective of the present research is to propose Cole-Hopf the transformation method (CHTM) and direct method (DM) based on discretization of the moving particle semi-implicit (MPS) method for solving the twodimensional Burgers’ equation. The numerical results of one and two-dimensional problems are compared with exact solutions and other numerical solutions, and the validity of the present methods is shown. Keywords: Burgers’ equation, Cole-Hopf transformation, direct method, discretization of MPS method, two-dimensional problem.
Keywords: Burgers’ equation, Cole-Hopf transformation, direct method,discretization of MPS method, two-dimensional problem.