Improvements to the Multi-Block Model
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.
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.