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2017•Journal of the Serbian Society for Computational MechanicsOpen access

DEVELOPMENT OF THE MESHLESS LOCAL PETROV-GALERKIN METHOD TO ANALYZE THREE-DIMENSIONAL TRANSIENT INCOMPRESSIBLE LAMINAR FLUID FLOW

M. J. Mahmoodabadi, F Mahmoodabadi, Meysam Atashafrooz

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Abstract

In this paper, a numerical algorithm is presented to simulate the three-dimensional transient incompressible flow using a meshless local Petrov-Galerkin (MLPG) method. In the proposed algorithm, the forward finite difference (FFD) and MLPG methods are employed for discretization of time derivatives and solving the Poisson equation of the pressure, respectively. The moving least-square (MLS) approximation is considered for interpolation, while the Gaussian weight function is used as a test function. Furthermore, the penalty approach is applied to satisfy the boundary conditions. Moreover, in two examples, the accuracy and efficiency of this approach is compared with the exact solutions.

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What this paper is about

In this paper, a numerical algorithm is presented to simulate the three-dimensional transient incompressible flow using a meshless local Petrov-Galerkin (MLPG) method. In the proposed algorithm, the forward finite difference (FFD) and MLPG methods are employed for discretization of time derivatives and solving the Poisson equation of the pressure, respectively. The moving least-square (MLS) approximation is considered for interpolation, while the Gaussian weight function is used as a test function. Furthermore, the penalty approach is applied to satisfy the boundary conditions. Moreover, in two examples, the accuracy and efficiency of this approach is compared with the exact solutions.

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Available abstract

In this paper, a numerical algorithm is presented to simulate the three-dimensional transient incompressible flow using a meshless local Petrov-Galerkin (MLPG) method. In the proposed algorithm, the forward finite difference (FFD) and MLPG methods are employed for discretization of time derivatives and solving the Poisson equation of the pressure, respectively. The moving least-square (MLS) approximation is considered for interpolation, while the Gaussian weight function is used as a test function. Furthermore, the penalty approach is applied to satisfy the boundary conditions. Moreover, in two examples, the accuracy and efficiency of this approach is compared with the exact solutions.

Key concepts: Petrov–Galerkin method, Laminar flow, Compressibility, Transient (computer programming), Regularized meshless method, Incompressible flow, Transient flow, Mathematics

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DEVELOPMENT OF THE MESHLESS LOCAL PETROV-GALERKIN METHOD TO ANALYZE THREE-DIMENSIONAL TRANSIENT INCOMPRESSIBLE LAMINAR FLUID FLOW — Research Paper | ScholarLens