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Improvements to the Multi-Block Model

Figure 1
Figure 1

This article highlights improvements that have been incorporated into the Multi-Block Model, to be included in the next release of FLOW-3D.

An important improvement of FLOW-3D's multi-block grid model has been incorporated into the code for release in Version 9.0. Multi-block gridding was first released with Version 8.0 to enable users to have a more efficient use of FLOW-3D's resources when modeling complex flow phenomena. However, some users complained of fluid volume losses at boundaries between mesh blocks. In its original formulation, the model employed a Dirichlet-type boundary condition (BC) for the solution of the Poisson equation for pressure. This is a “softer” solution system, allowing for faster convergence, but at the same time is less conserving of fluid volume.

multi-block example
Figure 2

In Version 9.0, when solving the continuity equation for pressure, two types of boundary conditions can be used at inter-block boundaries: a von Neumann type (where normal velocity is defined) or the Dirichlet type (where pressure is defined). Each type of BC has its cons and pros. The Neumann type gives a better conservation of mass, but, generally, has slower convergence and can result in a discontinuous pressure field. The new method applies both methods at the same time at all inter-block boundaries. A weighing factor, 0< α < 1.0, is used to define the portion of each type of BC. When α=0.0, then a pure Dirichlet type boundary condition is used and when α=1.0, then the Neumann type boundary condition is employed. A default value of α is 0.25 is given, as it seems to achieve a good local mass flux conservation and convergence for a wide variety of flows.

The new addition successfully addresses many of the reported fluid volume conservation problems. In addition, new diagnostics have been added to the pre-processor and solver. The former, reports the open areas between adjacent inter-block boundaries. This is useful to evaluate the quality of a multi-block grid – open areas at such boundaries should be as close as possible, generally, within 1%, to achieve good conservation of fluid volume.

In general, fluid volume is not conserved exactly due to small errors associated with spatial and temporal interpolation of the solution quantities at inter-block boundaries. A new solver diagnostic, multi-block volume error, reports the accumulated volume error due to these inaccuracies. The new quantity is automatically plotted as a function of time in the GUI's solver window and is also available for post-processing. For good accuracy the error should stay within a couple of percent. Figure 2 shows the multi-block volume error as a function of time for the MBLOCK example problem. It is clear that using a mixture of the Dirichlet and von Neumann type BC (a=0.25), instead of only Dirichlet (a=0.0), significantly reduces the overall volume error.