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In the present paper, a hybrid filter is introduced to simultaneously preserve the stability and accuracy and also to eliminate unwanted oscillations in the numerical simulation of shock-containing flows. The fourth-order compact finite difference scheme is used for the spatial discretization and the third-order Runge-Kutta scheme is used for the time integration. After each time-step, the hybrid filter is applied on the results. The filter is composed of a linear sixth-order filter and the dissipative part of the fifth-order weighted essentially non-oscillatory scheme. Using a shock-detecting sensor, the hybrid filter reduces to the linear sixth-order filter in smooth regions and to the fifth-order weighted essentially non-oscillatory filter in shock regions in order to eliminate unwanted oscillations produced by the non-dissipative spatial discretization method. The filter performance and accuracy of the results are examined through several test cases including the linear wave equation and one- and two-dimensional Euler equations of gas dynamics. The results are compared by that of a hybrid filter which is composed of the linear sixth-order and the second-order linear filter and that of the fifth-order weighted essentially non-oscillatory scheme.

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In this paper, an open-source software framework named “Chesmeh” for numerical solution of the fluid dynamics equations is introduced. The data structure is designed in a way that the software framework supports structured grids on arbitrary number of spatial dimensions. The software has the ability to decompose the numerical grid into several smaller grids for parallel processing. Furthermore, using some functions, the complexity of the parallel programming is considerably made easier for the user. The software is developed using the new features of the C++ programming language, specially the template metaprogramming feature. In addition to the linear finite difference schemes, which can be simply implemented, the nonlinear schemes such as essentially non-oscillatory shock capturing schemes are implemented. Using the software, it is also possible to use compact finite difference schemes, which lead to a tridiagonal system of equations. Defining and applying different kinds of boundary conditions are also predicted in the software. In addition, utilities are considered for file input and output. Using several test cases of compressible and incompressible flows and viscous and inviscid flows, the capabilities of the software are demonstrated.

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In the present article, a survey is carried out on the parallelization of several iterative solvers of the system of linear equations resulting from the discretization of the Poisson equation using the finite difference method. In particular, the point and line Gauss-Seidel successive over-relaxation methods, as well as the conjugate gradient and stabilized biconjugate gradient methods are investigated. For the over-relaxation methods, the optimum over-relaxation coefficient is used. The parallelization is first carried out on a multi-core central processor using C++ programming language and the OpenMP library, and then for a graphics processing unit using CUDA programming language. The results show, for both the two-dimensional and three-dimensional equations, the conjugate gradient methods due to a smaller number of iterations, have less computation time. Comparing the execution time of the different methods shows that for an 8-core processing, speedups of about 10 and 5 are achieved for the two- and three-dimensional equations, respectively. Furthermore, using a graphics processing unit leads to speedups between 5 and 10 in comparison to the 8-core processing.