Efficient solution for transient laminar mixed convection problems using semi-explicit DQ/RBF-DQM

Abstract

This article proposes a meshless, semi-explicit solution technique for time-dependent transient laminar mixed convection problems. The approach approximates both spatial and temporal derivatives using high-order differential quadrature rules, with spatial derivatives approximated using the radial basis function-based differential quadrature method (RBF-DQM) and temporal derivatives using the conventional global differential quadrature method (DQM). The method offers the unique ability to utilize DQM for both spatial and temporal derivatives of partial differential equations simultaneously. The RBF-DQM's meshless nature makes it suitable for irregular spatial domains, allowing for the analysis of problems with irregular geometries. The proposed algorithm was evaluated using transient laminar mixed convection simulations within both rectangular and irregular cavities, with results validated against benchmark solutions. The study concludes that the proposed algorithm is a reliable and accurate tool for the analysis of transient laminar mixed convection problems, with the added advantages of being easy to program and mesh-free, albeit with a need for suitable shape parameter selection.