SUMMARYThe numerical solution of the fluid flow governing equations requires the implementation of certain boundary conditions at suitable places to make the problem well-posed. Most of numerical strategies exhibit weak performance and obtain inaccurate solutions if the solution domain boundaries are not placed at adequate locations. Unfortunately, many practical fluid flow problems pose difficulty at their boundaries because the required information for solving the PDE's is not available there. On the other hand, large solution domains with known boundary conditions normally need a higher number of mesh nodes, which can increase the computational cost. Such difficulties have motivated the CFD workers to confine the solution domain and solve it using artificial boundaries with unknown flow conditions prevailing there. In this work, we develop a general strategy, which enables the control-volume-based methods to close the outflow boundary at arbitrary locations where the flow conditions are not known prior to the solution. In this regard, we extend suitable conservative statements at the outflow boundary. The derived statements gradually detect the correct boundary conditions at arbitrary boundaries via an implicit procedure using a finite element volume method. The extended statements are validated by solving the truncated benchmark backward-facing step problem. The investigation shows that the downstream boundary can pass through a recirculation zone without deteriorating the accuracy of the solution either in the domain or at its boundaries. The results indicate that the extended formulation is robust enough to be employed in solution domains with unknown boundary conditions.

SUMMARYThe finite-volume methods normally utilize either simple or complicated mathematical expressions to interpolate the fluxes at the cell faces of their unstructured volumes. Alternatively, we benefit from the advantages of both finite-volume and finite-element methods and estimate the advection terms on the cell faces using an inclusive pressure-weighted upwinding scheme extended on unstructured grids. The present pressure-based method treats the steady and unsteady flows on a collocated grid arrangement. However, to avoid a non-physical spurious pressure field pattern, two mass flux per volume expressions are derived at the cell interfaces. The dual advantages of using an unstructured-based discretization and a pressureweighted upwinding scheme result in obtaining high accurate solutions with noticeable progress in the performance of the primitive method extended on the structured grids. The accuracy and performance of the extended formulations are demonstrated by solving different standard and benchmark problems. The results show that there are excellent agreements with both benchmark and analytical solutions as well as experimental data.

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