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Received: 23 July 2018 Accepted: 28 August 2018 The solution of two-dimensional steady and transient fluid flow problem by the truly meshless local Petrov-Galerkin (MLPG) method has been addressed in the present article. The unknown function of velocity u(x) is approximated by moving least square approximant u(x). The essential boundary condition is imposed both by the direct and penalty function methods. Fourth order spline weight function, monomial basis function and a set of nonconstant coefficients are used to construct the approximants. The two-level  method is employed for temporal discretization. The results obtained by the MLPG method are compared with the analytical solution and also with the benchmark method results and found to be in the excellent agreement.

Numerical simulation of two-dimensional fluid flow problem using truly meshfree method