Implementation and verification of a two-dimensional CFD solver in Python for diffusive problems and laminar forced flows
DOI:
https://doi.org/10.37636/recit.v9n3e460Keywords:
Computational fluid dynamics, Finite volume method, ADI-SIMPLE algorithmsAbstract
Computational Fluid Dynamics (CFD) enables the prediction of the behavior of physical phenomena in a wide range of systems. In Mexico, its application has gained relevance in the study of energy-efficient buildings in response to the impacts of global warming. The objective of this work is to develop and verify a two-dimensional CFD solver implemented in the Python programming language, based on the finite volume method, capable of solving diffusive equations and the Navier-Stokes equations under laminar flow conditions, as well as to evaluate its computational performance. The numerical solution of the discretized governing equations is carried out using an Alternating Direction Implicit (ADI) method based on line Gauss-Seidel (LGS-ADI). The first case study corresponds to the solution of the steady-state heat conduction equation in a solid block. The second case consists of the simulation of laminar airflow in a square cavity filled with air, driven by a prescribed velocity at the top lid, with a Reynolds number of 1000. In this case, the SIMPLE algorithm is implemented for pressure-velocity coupling, and staggered grids are employed for the velocity field. The simulations are performed on a uniform 150x150 cell grid, initially using a first-order upwind scheme and subsequently a hybrid differencing scheme to reduce numerical diffusion. The results reproduce the characteristic flow structures, such as the formation of two vortices in the lower corners of the cavity, and show good agreement with the reference solution. The relative errors obtained in the verification cases are below 4.70%. Compared with a solver based on the classical Gauss-Seidel method, the ADI algorithm combined with the Thomas method reduces the computational time by 61.92% for the diffusive problem and by 15.04% for the forced flow problem, a difference attributed to the nonlinear nature of the latter. This work contributes to the development of an in-house code for numerical modeling using CFD.
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Copyright (c) 2026 Edgard Elohim Canche Cauich, Felipe Noh-Pat, Miguel Angel Gijón Rivera , Manuel Jesús Rodríguez-Pérez, Mauricio Iván Huchin-Miss
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