Volume 7, Issue 4
Local RBFs Based Collocation Methods for Unsteady Navier-Stokes Equations

Xueying Zhang, Xin An & C. S. Chen

Adv. Appl. Math. Mech., 7 (2015), pp. 430-440.

Published online: 2018-05

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  • Abstract

The local RBFs based collocation methods (LRBFCM) is presented to solve two-dimensional incompressible Navier-Stokes equations. In avoiding the illconditioned problem, the weight coefficients of linear combination with respect to the function values and its derivatives can be obtained by solving low-order linear systems within local supporting domain. Then, we reformulate local matrix in the global and sparse matrix. The obtained large sparse linear systems can be directly solved instead of using more complicated iterative method. The numerical experiments have shown that the developed LRBFCM is suitable for solving the incompressible Navier-Stokes equations with high accuracy and efficiency.

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@Article{AAMM-7-430, author = {Xueying Zhang, Xin An and C. S. Chen}, title = {Local RBFs Based Collocation Methods for Unsteady Navier-Stokes Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {7}, number = {4}, pages = {430--440}, abstract = {

The local RBFs based collocation methods (LRBFCM) is presented to solve two-dimensional incompressible Navier-Stokes equations. In avoiding the illconditioned problem, the weight coefficients of linear combination with respect to the function values and its derivatives can be obtained by solving low-order linear systems within local supporting domain. Then, we reformulate local matrix in the global and sparse matrix. The obtained large sparse linear systems can be directly solved instead of using more complicated iterative method. The numerical experiments have shown that the developed LRBFCM is suitable for solving the incompressible Navier-Stokes equations with high accuracy and efficiency.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2013.m337}, url = {http://global-sci.org/intro/article_detail/aamm/12056.html} }
TY - JOUR T1 - Local RBFs Based Collocation Methods for Unsteady Navier-Stokes Equations AU - Xueying Zhang, Xin An & C. S. Chen JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 430 EP - 440 PY - 2018 DA - 2018/05 SN - 7 DO - http://dor.org/10.4208/aamm.2013.m337 UR - https://global-sci.org/intro/aamm/12056.html KW - AB -

The local RBFs based collocation methods (LRBFCM) is presented to solve two-dimensional incompressible Navier-Stokes equations. In avoiding the illconditioned problem, the weight coefficients of linear combination with respect to the function values and its derivatives can be obtained by solving low-order linear systems within local supporting domain. Then, we reformulate local matrix in the global and sparse matrix. The obtained large sparse linear systems can be directly solved instead of using more complicated iterative method. The numerical experiments have shown that the developed LRBFCM is suitable for solving the incompressible Navier-Stokes equations with high accuracy and efficiency.

Xueying Zhang, Xin An & C. S. Chen. (1970). Local RBFs Based Collocation Methods for Unsteady Navier-Stokes Equations. Advances in Applied Mathematics and Mechanics. 7 (4). 430-440. doi:10.4208/aamm.2013.m337
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