Numerical solution strategy for natural convection problems in a triangular cavity using a direct meshless local Petrov-Galerkin method combined with an implicit artificial-compressibility model

Abstract

Thermal analysis of natural convection in a cavity is solved by numerical approach. The direct meshless local Petrov–Galerkin method combined with an implicit artificial-compressibility model is proposed here to simulate laminar natural convective heat transfer in triangular cavities. The spatial terms of the governing equation are discretized using the direct meshless local Petrov–Galerkin method with the Dirac function as the test function. The method uses an artificial-compressibility scheme to couple the pressure with the velocity components directly. The semi-algebraic system is solved using an implicit backward Euler pseudo-time method. Kovasznay flow problem is presented to examine the accuracy of proposed method. The validation of the obtained results by using experimental data is also provided, and four test problems — natural convection in an equilateral triangular cavity, a right-angled triangular cavity, an isosceles triangular cavity, and an irregular triangular cavity — are solved by using the proposed method. The numerical results obtained using the proposed method showed excellent agreement with those obtained using the conventional methods available in the literature.