9427163163

LA. Bueno. et al., Int. J. Comp. Meth. and Exp. Meas., Vol. 5, No. 3 (2017) 359-368

A COUPLED LOCALIZED RBF MESHLESS/DRBEM FORMULATION FOR ACCURATE MODELING OF INCOMPRESSIBLE FLUID FLOWS

LEONARDO A. BUENO¹. EDUARDO A. DlVO' & ALAIN J. KASSAB²'Department of Mechanical Engineering, Embry-Riddle Aeronautical University, Daytona Beach, FL, USA. ²Department of Mechanical and Aerospace Engineering University of Central Florida. Orlando, FL, USA.

ABSTRACT

Velocity-pressure coupling schemes for the solution of incompressible fluid flow problems in Computational Fluid Dynamics (CFD) rely on the formulation of Poisson-like eąuations through projection methods. The solution of these Poisson-like equations represent the pressure correction and the velocity correction to ensurc proper satisfaction of the conservation of mass equation at each step of a time-marching scheme or at each levcl of an iteration process. Inaccurate Solutions of these Poisson-like equations result in meaningless instantaneous or intermediate approximations that do not represent the proper time-accurate behavior of the flow. The fact that these equations must be solved to convergence at every step of the overall solution process introduces a major bottleneck for the efficiency of the method. We present a formulation that achieves high levels of accuracy and effi-ciency by properly solving the Poisson equations at each step of the solution process by formulating a Localized RBF Collocation Meshless Method (LRC-MM) solution approach for the approxima-tion of the diffusive and convective derivatives while employing the same framework to implement a Dual-Reciprocity Boundary Element Method (DR-BEM) for the solution of the ensuing Poisson equations. The same boundary discretization and point distribution employed in the LRC-MM is used for the DR-BEM. The methodology is implemented and tested in the solution of a baekward-facing step problem.

Keywords: dual reciprocity boundary element method, incompressible fluid flows, meshless methods, radial basis functions.

1 INTRODUCTION

Meshless methods are numerical techniques that utilize interpolation, either global or localized, on a set of non-ordered points, see [1, 2]. These are being used to resolve complex problems, such as flow transport problems, see [3J. There are several advantages to them such as accuracy control, sińce additional nodes madę be added where needed, and a morę accurate representation of the objects through meshfree discretization, see [4]. The principal reason for such flcxibility is that the nodes do not nced to conformant to the geometry and sińce elements are not used to join the nodes, degeneration is a non-issue. This is a direct contrast to meshed techniqucs, which rcquircd that nodc connectivity follows the boundary contours and thus there is a need to have well-shaped elements, see [51. Truły meshless methods do not require any mesh or particular node distribution. Global radial-basis function (RBF) interpolation meshless methods are computationally expensive and require special treatment to deal with poor conditioning in the algebraic set of equations. The localized RBF collocation meshless methods (LRC-MM) address the issues that arisc from the global RBF approach, see f 1,6]. LRC-MM have been implemented in the solution of incompressible fluid flows cffcctivcly adapting upwinding schemes for convcctivc-dominatcd flows, see f 1, 3, 5, 6]. However, in decoupling the governing equations for incompressible fluid flows, a Poisson-like equation arises for the solution of the pressure field at each time step. Although ©2017 WIT Press, www.witpress.com

ISSN: 2046-0546 (paper format), ISSN: 2046-0554 (online), http://www.witpress.com/journals DOI: 10.2495/CMEM-Y5-N3-359-368