Using fully implicit conservative statements to close open boundaries passing through recirculations

Abstract

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.

Global volume conservation in unsteady free surface flows with energy absorbing far‐end boundaries

“…Appropriate boundary conditions for velocity and pressure must be devised for an open boundary at the far-end of the computational domain [8]. In flows without free surface, outflow boundary conditions have been thoroughly studied for different flow conditions [9][10][11]. In free surface flows, surface waves introduce additional complexity in the far-end.…”

A lagged implicit segregated data reconstruction procedure to treat open boundaries

“…One way is using the shape function tool as in finite element method, e.g. [17,19]. The other is based on interpolation using the neighboring points where approximate data are available (usually with distance weighting).…”

“…The proposed procedure is equally applicable to coupled solvers without shape function tool. This type of OBC, like the work of Darbandi et al [17] and Papanastasiou et al [12], is suitable to study upstream domains of interest in problems whose physics show that the solution in that domain is not highly affected by the downstream events. One of such problems is shown in Fig.…”

“…Their idea is interesting since it essentially extends the validity of the discretized governing equations to the boundary. Currently Darbandi et al [15][16][17] applied and successively improved the application of this type of open boundary condition in their co-located pressure based coupled finite volume procedure. In essence, they have developed a coupled finite volume procedure based on the finite element shape function data reconstruction and have applied free boundary condition in an implicit fully conservative manner.…”

Developing a unified FVE‐ALE approach to solve unsteady fluid flow with moving boundaries

“…The terms inside the lhs parentheses are discretized using the gradients of FE shape functions; see Equation (23). After suitable discretizations of all the terms, they are substituted in Equation (27).…”