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Showing 3 results for Upwind
K. Mazaheri, M. Darbandi, S. Vakilipour,
Volume 6, Issue 1 (9-2006)
Abstract
Two essential steps in numerical simulation of a flow field are discretization of the computational space and discretization of the governing partial differential equations (pde’s). In the present work a triangular unstructured grid is utilized. Unstructured grids are recognized to be superior for complex geometries as well as for grid adaptation. For descritization of governing pde’s a finite element method is employed. This research presents a new implicit finite element method in a triangular unstructured grid. For convection term of Navier–Stokes equation a conservative upwind method is used, while a finite element method is used for viscous terms. Results are very promising for viscous flows inside a driven cavity.
Shidvash Vakilipour, Masoud Mohammadi, Rouzbeh Riazi,
Volume 16, Issue 10 (1-2017)
Abstract
The main task in finite volume methods (FVM) is to estimate proper values on the cell faces based on the calculated values on the nodes or cell centers. In this way, upwinding schemes are the most successful schemes for estimation of values on the control volume faces. These schemes have been developed in FVM for various techniques with proper accuracy on different kinds of structured and unstructured grids. In this research, the physical influence scheme (PIS) is developed to the cell-centered FVM in an implicit coupled solver and the results are compared with other two main branches of upwinding methods: exponential differencing scheme (EDS) and skew upwind differencing scheme (SUDS). Accuracy of these schemes is evaluated in lid-driven cavity flow at Re = 400-10000 and backward-facing step flow at Re = 800. Simulations show considerable difference between the of results EDS scheme with benchmarks, especially for lid-driven cavity flow at high Reynolds numbers which occurs due to false diffusion. Comparing SUDS and PIS schemes shows relatively close results in backward-facing step flow and different results in lid-driven cavity flow. The poor results of SUDS in cavity flow can be related to its non-pressure sensitivity between cell face and upwind points which is critical for such vortex dominant flows. Instead, the PIS scheme by applying a momentum equation between the cell face and upwind points, is able to capture flow vortices properly and matching well with benchmarks.
Mohammad Reza Saremi Tehrani, Mohsen Ghadyani, Vali Enjilela,
Volume 24, Issue 3 (2-2024)
Abstract
In this study, a new upwind scheme has been used to solve the continuous Boltzmann equation and to develop its application in the effective solution of incompressible flows. Time derivative in the Boltzmann equation has been discretized using the first-order forward finite difference scheme. The spatial derivatives in the Boltzmann equation have been discretized using this new scheme. Further, the combined effects of the upwind differential mechanism along with the finite difference method are presented to enhancement the stability of the standard lattice Boltzmann method in solving problems with high Reynolds numbers. To confirm the validation of the proposed method, one unsteady problem, this has an analytical solution, and two incompressible steady problems which have not analytical solutions, have been solved numerically. The first benchmark problem is the conductive heat transfer on a slab and two last problems are flow over a flat plate and flow in a lid-driven cavity. In order to check the numerical accuracy and stability of the proposed method, the results have been compared with the standard lattice Boltzmann method and the finite difference lattice Boltzmann method. The proposed method guarantees that without applying the filtering method, more stable and accurate results are obtained compared with the finite difference lattice Boltzmann method. The simulation results show the effectiveness of the present method and its appropriate compatibility with analytical solutions and other numerical methods.
