Cálculo del flujo difusivo en dominios complejos mediante el método de volúmenes finitos
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Universidad Industrial de Santander
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Este artículo describe una estrategia de discretización de la ecuación de difusión en mallas no estructuradas aplicando el método de los volúmenes finitos con las variables calculadas en el centroide de cada volumen. Esta aproximación está basada en el trabajo de Date [1] que usa una técnica iterativa conocida como corrección diferida para solucionar el cálculo del flujo difusivo en mallas no ortogonales. Se comprobó que para ángulos internos del elemento menores a 50°, el método propuesto por Date no converge y entonces se propone una nueva forma de calcular el gradiente que favorece la convergencia del problema. Se muestra un estudio de la convergencia donde se demuestra la alta efectividad del método propuesto. A partir de la solución de un problema típico, basado en la solución de la ecuación de Poisson, se realizó la comparación de los resultados obtenidos con los de la solución analítica, donde se observó una alta correspondencia de los resultados sin comprometer el tiempo de cálculo. Finalmente, se demostró la flexibilidad de la aproximación implementada al realizar simulaciones sobre mallas estructuradas y no estructuradas, usando elementos en forma de cuadriláteros y triángulos en 2D, y cubos curvilíneos y tetraedros en 3D.
This paper describes a strategy to discretize the Poisson equation on unstructured meshes using the finite volume method based on the center of the cells. This approach is based on Date’s work[1] that uses an iterative technique known as deferred correction to obtain the right diffusive flow field in no orthogonal meshes. It was found that the method proposed by Date does not converge when the internal angles are less than 40°, then we proposes a new way to calculate the gradient in order to ensure the convergence. It shows a convergence study that demonstrates the high effectiveness of the proposed method. After solving a typical problem, based on the solution of the Poisson equation, we compared the results obtained with the analytical solution, where there was a high correspondence of results without compromising the computational time. Finally, we have demonstrate the flexibility of the approach implemented by performing simulations on structured and unstructured meshes, using elements in the form of quadrilaterals and triangles in 2D, and curvilinear cubes and tetrahedrons in 3D.
This paper describes a strategy to discretize the Poisson equation on unstructured meshes using the finite volume method based on the center of the cells. This approach is based on Date’s work[1] that uses an iterative technique known as deferred correction to obtain the right diffusive flow field in no orthogonal meshes. It was found that the method proposed by Date does not converge when the internal angles are less than 40°, then we proposes a new way to calculate the gradient in order to ensure the convergence. It shows a convergence study that demonstrates the high effectiveness of the proposed method. After solving a typical problem, based on the solution of the Poisson equation, we compared the results obtained with the analytical solution, where there was a high correspondence of results without compromising the computational time. Finally, we have demonstrate the flexibility of the approach implemented by performing simulations on structured and unstructured meshes, using elements in the form of quadrilaterals and triangles in 2D, and curvilinear cubes and tetrahedrons in 3D.
Keywords
CFD, diffusive flux, complex domain, finite volume method, CFD, flujo difusivo, dominio complejo, mallas no estructuradas, volúmenes finitos, unstructured meshes