A meshless radial basis function based method for modeling dual-phase-lag heat transfer in irregular domains

2021 ◽  
Vol 85 ◽  
pp. 1-17
Author(s):  
Ji Lin ◽  
Hao Yu ◽  
Sergiy Reutskiy ◽  
Yuan Wang
Keyword(s):  
Heat Transfer ◽  
Radial Basis Function ◽  
Basis Function ◽  
Phase Lag ◽  
Dual Phase ◽  
Irregular Domains ◽  
Radial Basis

An Efficient Localized RBF Meshless Method Applied to FLuid Flow and Conjugate Heat Transfer

2005 ◽  
Author(s):  
Eduardo Divo ◽  
Alain J. Kassab
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Viscous Fluid ◽  
Radial Basis Function ◽  
Basis Function ◽  
Meshless Method ◽  
Conjugate Heat Transfer ◽  
Implicit Time ◽  
Viscous Fluid Flow ◽  
Radial Basis

A localized radial basis function (RBF) meshless method is developed for coupled viscous fluid flow and convective heat transfer problems. The method is based on new localized radial-basis function (RBF) expansions using Hardy Multiquadrics for the sought-after unknowns. An efficient set of formulae are derived to compute the RBF interpolation in terms of vector products thus providing a substantial computational savings over traditional meshless methods. Moreover, the approach developed in this paper is applicable to explicit or implicit time marching schemes as well as steady-state iterative methods. We apply the method to viscous fluid flow and conjugate heat transfer (CHT) modeling. The incompressible Navier-Stokes are time marched using a Helmholtz potential decomposition for the velocity field. When CHT is considered, the same RBF expansion is used to solve the heat conduction problem in the solid regions enforcing temperature and heat flux continuity of the solid/fluid interfaces. The computation is accelerated by distributing the load over several processors via a domain decomposition along with an interface interpolation tailored to pass information through each of the domain interfaces to ensure conservation of field variables and derivatives. Numerical results are presented for several cases including channel flow, flow in a channel with a square step obstruction, and a jet flow into a square cavity. Results are compared with commercial computational fluid dynamics code predictions. The proposed localized meshless method approach is shown to produce accurate results while requiring a much-reduced effort in problem preparation in comparison to other traditional numerical methods.

An Efficient Localized Radial Basis Function Meshless Method for Fluid Flow and Conjugate Heat Transfer

2006 ◽  
Vol 129 (2) ◽  
pp. 124-136 ◽  
Author(s):  
Eduardo Divo ◽  
Alain J. Kassab
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Viscous Fluid ◽  
Radial Basis Function ◽  
Basis Function ◽  
Meshless Method ◽  
Conjugate Heat Transfer ◽  
Implicit Time ◽  
Viscous Fluid Flow ◽  
Radial Basis

A localized radial basis function (RBF) meshless method is developed for coupled viscous fluid flow and convective heat transfer problems. The method is based on new localized radial-basis function (RBF) expansions using Hardy Multiquadrics for the sought-after unknowns. An efficient set of formulae are derived to compute the RBF interpolation in terms of vector products thus providing a substantial computational savings over traditional meshless methods. Moreover, the approach developed in this paper is applicable to explicit or implicit time marching schemes as well as steady-state iterative methods. We apply the method to viscous fluid flow and conjugate heat transfer (CHT) modeling. The incompressible Navier–Stokes are time marched using a Helmholtz potential decomposition for the velocity field. When CHT is considered, the same RBF expansion is used to solve the heat conduction problem in the solid regions enforcing temperature and heat flux continuity of the solid/fluid interfaces. The computation is accelerated by distributing the load over several processors via a domain decomposition along with an interface interpolation tailored to pass information through each of the domain interfaces to ensure conservation of field variables and derivatives. Numerical results are presented for several cases including channel flow, flow in a channel with a square step obstruction, and a jet flow into a square cavity. Results are compared with commercial computational fluid dynamics code predictions. The proposed localized meshless method approach is shown to produce accurate results while requiring a much-reduced effort in problem preparation in comparison to other traditional numerical methods.

scholarly journals Symmetric Radial Basis Function Method for Simulation of Elliptic Partial Differential Equations

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 327 ◽  
Author(s):  
Phatiphat Thounthong ◽  
Muhammad Khan ◽  
Iltaf Hussain ◽  
Imtiaz Ahmad ◽  
Poom Kumam
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Function Method ◽  
Three Dimensional ◽  
Elliptic Partial Differential Equations ◽  
Elliptic Pdes ◽  
Irregular Domains ◽  
Numerical Tests ◽  
Radial Basis ◽  
Radial Basis Function Method

In this paper, the symmetric radial basis function method is utilized for the numerical solution of two- and three-dimensional elliptic PDEs. Numerical results are obtained by using a set of uniform or random points. Numerical tests are accomplished to demonstrate the efficacy and accuracy of the method on both regular and irregular domains. Furthermore, the proposed method is tested for the solution of elliptic PDE in the case of various frequencies.

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