Two-step Taylor-characteristic-based MLPG method for fluid flow and heat transfer applications

Enjilela, Vali; Arefmanesh, A.

doi:10.1016/j.enganabound.2014.10.012

Cited by 16 publications

(5 citation statements)

References 43 publications

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“…However, for unsteady flow, the stability condition of the dual‐time stepping procedure and the choice of the AC parameter can become too restrictive, even leading to slow convergence rates. Based on the midpoint method, Bao and Zhou and Enjilela and Arefmanesh further proposed the two‐step method, hybrid MINI element, and pressure projection method in order to improve the accuracy of the CBS method and stable the pressure field, but the two‐step method needs to update total element matrix twice in each time step, which reduce calculation efficiency. In order to further improve calculation accuracy, Drikakis et al used the classic Runge‐Kutta method for temporal discretization, but spacial discretization is based on the upwind difference scheme to stabilize the pressure field.…”

Section: Introductionmentioning

confidence: 99%

A Galerkin finite element algorithm based on third‐order Runge‐Kutta temporal discretization along the uniform streamline for unsteady incompressible flows

Liao

Zhang

Chen

2019

Numerical Methods in Fluids

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Summary In this paper, for two‐dimensional unsteady incompressible flow, the Navier‐Stokes equations without convection term are derived by the coordinate transformation along the streamline characteristic. The third‐order Runge‐Kutta method along the streamline is introduced to discrete the alternative Navier‐Stokes equations in time, and spacial discretization is carried out by the Galerkin method, and then, the third‐order accuracy finite element method is obtained. Meanwhile, the streamline velocity is uniformly approximated by initial velocity in each time step in order to reduce update frequency of total element matrix and improve calculation efficiency. Finally, some classic unsteady flow examples are calculated and analyzed by different calculation methods, which further demonstrate that the present method has more advantages in stability, permissible time step, dissipation, computational cost, and accuracy. The code can be downloaded at https://doi.org/10.13140/RG.2.2.27706.44484.

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Section: Introductionmentioning

confidence: 99%

A Galerkin finite element algorithm based on third‐order Runge‐Kutta temporal discretization along the uniform streamline for unsteady incompressible flows

Liao

Zhang

Chen

2019

Numerical Methods in Fluids

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“…Bao [28] and Enjilela [29] proposed the two-step method and the pressure projection method in order to improve calculation accuracy and stabilize pressure field. Based on semi-implicit CBS procedures, Chen [30] derived a cell-based smoothed finite element method, which has merits on better robustness against distorted mesh with only slight more computation time.…”

Section: Introductionmentioning

confidence: 99%

Runge-Kutta Finite Element Method Based on the Characteristic for the Incompressible Navier-Stokes Equations

sci¹

2019

AAMM

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In this paper, a finite element method based on the characteristic for the incompressible Navier-Stokes equations is proposed by introducing Runge-Kutta method. At first, coordinate transformation operation is performed to obtain the alternative Navier-Stokes equations without convection term. Then, instead of the classical characteristic-based split (CBS) method, we use the third-order Runge-Kutta method along the characteristic to carry out time discretization in order to improve calculation accuracy, and segregate the calculation of the pressure from that of the velocity based on the momentum-pressure Poisson equation method. Finally, some classical benchmark problems are used to validate the effectiveness of the present method. Compared with the classical method, the present method has lower dissipation, larger permissible time step, and higher time accuracy. The code can be downloaded at

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“…Simulation of two-dimensional unsteady incompressible flow is done by the MLPG method and with a forward difference scheme for the time derivatives in Sataprahm and Luadsong (2014). In one of the latest researches, Enjilela and Arefmanesh proposed a stabilized two-step Taylorcharacteristic-based MLPG method to solve laminar fluid flow and heat transfer problems (Enjilela and Arefmanesh 2015). The results of that work shown that very good agreements exist between the results obtained using the proposed meshless method with those obtained using the conventional methods.…”

Section: Introductionmentioning

confidence: 99%

Development of the Meshless Local Petrov-Galerkin Method to Analyze Three-Dimensional Transient Incompressible Laminar Fluid Flow

Mahmoodabadi¹,

Mahmoodabadi²,

Atashafrooz³

2018

JSSCM

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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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Two-step Taylor-characteristic-based MLPG method for fluid flow and heat transfer applications

Cited by 16 publications

References 43 publications

A Galerkin finite element algorithm based on third‐order Runge‐Kutta temporal discretization along the uniform streamline for unsteady incompressible flows

A Galerkin finite element algorithm based on third‐order Runge‐Kutta temporal discretization along the uniform streamline for unsteady incompressible flows

Runge-Kutta Finite Element Method Based on the Characteristic for the Incompressible Navier-Stokes Equations

Development of the Meshless Local Petrov-Galerkin Method to Analyze Three-Dimensional Transient Incompressible Laminar Fluid Flow

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