Boundary integral equation formulations for steady Navier-Stokes equations using the Stokes fundamental solutions

1985 ◽  
Vol 2 (3) ◽  
pp. 128-132 ◽  
Author(s):  
Nobuyoshi Tosaka ◽  
Kazuei Onishi
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Stokes Equations ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Navier Stokes ◽  
Navier Stokes Equations

Meshless velocity – vorticity local boundary integral equation (LBIE) method for two dimensional incompressible Navier-Stokes equations

2019 ◽  
Vol 29 (11) ◽  
pp. 4034-4073 ◽  
Author(s):  
E.J. Sellountos ◽  
Jorge Tiago ◽  
Adelia Sequeira
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Stokes Equations ◽  
Boundary Integral ◽  
Integral Representations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Local Boundary ◽  
Local Boundary Integral Equation

Purpose This paper aims to describe the 2D meshless local boundary integral equation (LBIE) method for solving the Navier–Stokes equations. Design/methodology/approach The velocity–vorticity formulation is selected to eliminate the pressure gradient of the equations. The local integral representations of flow kinematics and transport kinetics are derived. The integral equations are discretized using the local RBF interpolation of velocities and vorticities, while the unknown fluxes are kept as independent variables. The resulting volume integrals are computed using the general radial transformation algorithm. Findings The efficiency and accuracy of the method are illustrated with several examples chosen from reference problems in computational fluid dynamics. Originality/value The meshless LBIE method is applied to the 2D Navier–Stokes equations. No derivatives of interpolation functions are used in the formulation, rendering the present method a robust numerical scheme for the solution of fluid flow problems.

Boundary Integral Equation Formulation in Generalized Linear Thermo-Viscoelasticity With Rheological Volume

2003 ◽  
Vol 70 (5) ◽  
pp. 661-667 ◽  
Author(s):  
A. S. El-Karamany
Keyword(s):  
Integral Equation ◽  
Rheological Properties ◽  
Boundary Integral Equation ◽  
Relaxation Times ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Phase Lag ◽  
Integral Equation Formulation ◽  
Special Cases ◽  
The Given

A general model of generalized linear thermo-viscoelasticity for isotropic material is established taking into consideration the rheological properties of the volume. The given model is applicable to three generalized theories of thermoelasticity: the generalized theory with one (Lord-Shulman theory) or with two relaxation times (Green-Lindsay theory) and with dual phase-lag (Chandrasekharaiah-Tzou theory) as well as to the dynamic coupled theory. The cases of thermo-viscoelasticity of Kelvin-Voigt model or thermoviscoelasticity ignoring the rheological properties of the volume can be obtained from the given model. The equations of the corresponding thermoelasticity theories result from the given model as special cases. A formulation of the boundary integral equation (BIE) method, fundamental solutions of the corresponding differential equations are obtained and an example illustrating the BIE formulation is given.

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