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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.

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In this paper two automated and robust algorithms for generation of unstructured grids suitable for miltiscale finite volume method in oil reservoirs is presented. The multiscale finite volume method is an efficient numerical method for flow simulation in porous media. The multiscale finite volume method has been extensively studied on structured grids. In this research multiscale finite volume method is extended to unstructured grids. Development of the MSFV method to unstructured grids provides advantages of flexibility and compatibility with geological structures. In this method calculations are carried out on three grids, fine grid, primal coarse grid and dual coarse grid. One of the main challenges to extend the multiscale finite volume method to unstructured grids is to generate primal and dual coarse grids. In this paper an algorithm for partitioning of unstructured grid and generating primal coarse grid is proposed. Also a new algorithm for generating dual coarse grid is presented. Finally, the proposed algorithms for generating multiscale unstructured grids are employed for flow simulations in porous media. Numerical results show that the multiscale finite volume method with generated multiscale unstructured grids of this research can accurately predict the fine scale solution.

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The growing and diverse applications of low Reynolds number operating vehicles impose the need for their accurate study. Optimization is an important part of computational science that can improve the performance and increase the efficiency of the initial geometry. most of the research studies on aerodynamic optimization were focused on high Reynolds number airfoils. But for aerodynamic devices that have small dimensions, like MAVs, usually the flow speed is low and thus the unsteady effects caused by boundary layer separation cannot be neglected. In this article, oscillating airfoil with pitching motion in turbulent and low Reynolds flow has been optimized with the continuous adjoint method. Drag to lift ratio was chosen to be the objective function and free form deformation parameters is adopted for the surface geometry perturbations. Since aerodynamic optimization generally consists of two parts, first solving the flow equation and then computing the gradient of the objective function, in this article in order to evaluate the accuracy of the optimization process both has been validated. The results show that the adjoint equation converges well and with specifying the suitable constraints, the designed shape approaches to the most optimized level without the loss of performance.

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Abstract In this paper, a viscous all-speed flow solver has been developed based on Roe upwind scheme in unstructured database. In the presented method, stiffness of the compressible governing equations in low-speed region reduces using the preconditioning form. In calculating the artificial viscosity of a Roe upwind scheme, multiple matrices multiplication are needed. Frink reduced these costly operations by simplification of the matrices multiplication to some flux components which are related to distinct eigenvalues. In this research similar to Frink work, the equations of artificial viscosity in preconditioning Roe upwind scheme obtained and presented in the flux components form. This is a generalized form that can be easily switched to the preconditioned or non-preconditioned form. This is useful in converting any original Roe upwind scheme to the preconditioning form and also has application in adjoint optimization method. Results of the computer code were compared with experimental data of single and two-element airfoils in both preconditioning and non-preconditioning form. The results show that the non-preconditioning compressible solver hardly converged in low-speed regions while the preconditioned form converged more rapidly.