## 16.1. Hybrid and Conservative Variable Values

The CFX-Solver calculates the solution to your CFD problem using polyhedral finite volumes surrounding the vertices of the underlying mesh elements (hexahedrons, tetrahedrons, prisms, pyramids). Analytical solutions to the Navier-Stokes equations exist for only the simplest of flows under ideal conditions. To obtain solutions for real flows, a numerical approach must be adopted whereby the equations are replaced by algebraic approximations that may be solved using a numerical method.

The solution values on the boundary vertices, called conservative values, are the values obtained from solving the conservation equations for the boundary control volumes. These values are not necessarily the same as the specified boundary condition values, although the specified boundary value is used to close boundary fluxes for the boundary control volume. For example, on a no-slip wall, the wall velocity is used to compute the viscous force for the boundary face of the boundary control volume, but the resulting control volume equation solution will not necessarily be the wall velocity. The conservative values are representative of the boundary control volume, not the boundary itself. For visualization purposes, it is often useful to view the specified boundary condition value for the boundary vertices rather than the conservative values. This is especially true when the value of a conservative solution variable (such as pressure or temperature, for instance) is specified at a particular boundary condition. The specified boundary values are called hybrid values. CFD-Post uses hybrid values by default for most variables. Hybrid values are obtained by overwriting the conservative results on the boundary nodes produced by the CFX-Solver with values based on the specified boundary conditions. This ensures, for example, that the velocity is displayed as zero on no-slip walls. For quantitative calculations, the conservative values should normally be used because they are consistent with the discrete solutions obtained by the solver. If you want to use these values in CFD-Post, you can select them from the Variables Editor dialog box as described above. By default, CFD-Post uses conservative values when the Calculate command is used.

The difference between hybrid and conservative values at wall boundaries can be demonstrated using the following figure:

Using velocity as an example, the velocity value calculated at a mesh node is based upon the ‘average’ in the control volume surrounding that node. For calculation purposes, the entire control volume is then assumed to possess that velocity. At a boundary node, its surrounding control volume includes an area in the bulk of the fluid (this area is highlighted around the boundary node marked 1). Hence, the conservative velocity calculated at the wall node is not zero, but an ‘average’ over the control volume adjacent to the boundary. At a wall boundary node the difference between conservative and hybrid values can be illustrated by considering the case of the mass flow rate through the wall-adjacent control volume. If a zero velocity was enforced at the boundary node, then this would produce zero mass flow through the control volume, which is clearly not correct.

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