TY - JOUR

T1 - A meshless scheme for incompressible fluid flow using a velocity-pressure correction method

AU - Bourantas, G. C.

AU - Loukopoulos, V. C.

PY - 2013/12/15

Y1 - 2013/12/15

N2 - A meshless point collocation method is proposed for the numerical solution of the steady state, incompressible Navier-Stokes (NS) equations in their primitive u-v-p formulation. The flow equations are solved in their strong form using either a collocated or a semi-staggered "grid" configuration. The developed numerical scheme approximates the unknown field functions using the Moving Least Squares approximation. A velocity, along with a pressure correction scheme is applied in the context of the meshless point collocation method. The proposed meshless point collocation (MPC) scheme has the following characteristics: (i) it is a truly meshless method, (ii) there is no need for pressure boundary conditions since no pressure constitutive equation is solved, (iii) it incorporates simplicity and accuracy, (iv) results can be obtained using collocated or semi-staggered "grids", (v) there is no need for the usage of a curvilinear system of coordinates and (vi) it can solve steady and unsteady flows. The lid-driven cavity flow problem, for Reynolds numbers up to 5000, has been considered, by using both staggered and collocated grid configurations. Following, the Backward-Facing Step (BFS) flow problem was considered for Reynolds numbers up to 800 using a staggered grid. As a final example, the case of a laminar flow in a two-dimensional tube with an obstacle was examined.

AB - A meshless point collocation method is proposed for the numerical solution of the steady state, incompressible Navier-Stokes (NS) equations in their primitive u-v-p formulation. The flow equations are solved in their strong form using either a collocated or a semi-staggered "grid" configuration. The developed numerical scheme approximates the unknown field functions using the Moving Least Squares approximation. A velocity, along with a pressure correction scheme is applied in the context of the meshless point collocation method. The proposed meshless point collocation (MPC) scheme has the following characteristics: (i) it is a truly meshless method, (ii) there is no need for pressure boundary conditions since no pressure constitutive equation is solved, (iii) it incorporates simplicity and accuracy, (iv) results can be obtained using collocated or semi-staggered "grids", (v) there is no need for the usage of a curvilinear system of coordinates and (vi) it can solve steady and unsteady flows. The lid-driven cavity flow problem, for Reynolds numbers up to 5000, has been considered, by using both staggered and collocated grid configurations. Following, the Backward-Facing Step (BFS) flow problem was considered for Reynolds numbers up to 800 using a staggered grid. As a final example, the case of a laminar flow in a two-dimensional tube with an obstacle was examined.

KW - Incompressible flow

KW - Meshless method

KW - MLS

KW - Strong form

KW - Velocity-pressure correction

UR - http://www.scopus.com/inward/record.url?scp=84885072034&partnerID=8YFLogxK

U2 - 10.1016/j.compfluid.2013.09.010

DO - 10.1016/j.compfluid.2013.09.010

M3 - Article

AN - SCOPUS:84885072034

SN - 0045-7930

VL - 88

SP - 189

EP - 199

JO - Computers and Fluids

JF - Computers and Fluids

ER -