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ARTICLE

Low and Intermediate Re Solution of Lid Driven Cavity Problem by Local Radial Basis Function Collocation Method

by K. Mramor¹, R. Vertnik², B. Šarler¹

1 COBIK, Solkan, Slovenia.
2 Štore Steel, Štore, Slovenia.
3 University of Nova Gorica, Nova Gorica, Slovenia.
4 Institute of Metals and Technology, Ljubljana, Slovenia.
5 Corresponding author: Professor Božidar Šarler, email: bozidar.sarler@ung.si

Computers, Materials & Continua 2013, 36(1), 1-21. https://doi.org/10.3970/cmc.2013.036.001

Abstract

This paper explores the application of Local Radial Basis Function Collocation Method (LRBFCM) [Šarler and Vertnik (2006)] for solution of Newtonian incompressible 2D fluid flow for a lid driven cavity problem [Ghia, Ghia, and Shin (1982)] in primitive variables. The involved velocity and pressure fields are represented on overlapping five-noded sub-domains through collocation by using Radial Basis Functions (RBF). The required first and second derivatives of the fields are calculated from the respective derivatives of the RBF’s. The momentum equation is solved through explicit time stepping. The method is alternatively structured with multiquadrics and inverse multiquadrics RBF’s. In addition, two different approaches are used for pressure velocity coupling (Fractional Step Method (FSM) [Chorin (1968)] and Artificial Compressibility Method (ACM) [Chorin (1967)] with Characteristic Based Split (CBS) [Zienkiewicz and Codina (1995); Zienkiewicz, Morgan, Sai, Codina and Vasquez (1995)]). The method is tested for several low and intermediate Reynolds numbers (100, 400, 1000 and 3200) and node arrangements (41x41, 81x81, 101x101, 129x129). The original contribution of the paper represents extension of the LRBFCM to Reynolds number beyond 400 and assessment of the method for two different types of RBFs and two different types of pressure-velocity couplings. The obtained numerical results, in terms of mid-plane velocities, are in a good agreement with the data calculated in several reference publications and by commercial code. Both RBF’s used give approximately the same results. Both pressure-velocity coupling methods give approximately the same results, however the FSM turns out to be slightly more efficient. The advantages of the method are simplicity, accuracy and straightforward applicability in non-uniform node arrangements.

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