## 4.1. Equation Residual

CFX-Solver calculates the solution to various equations, given the appropriate boundary conditions and models for your particular CFD problem. For details, see Governing Equations in the CFX-Solver Theory Guide.

At any stage of a calculation, each equation will not be satisfied exactly, and the “residual” of an equation identifies how much the left-hand-side of the equation differs from the right-hand-side at any point in space. If the solution is “exact,” then the residual is zero. This means that each of the relevant finite volume equations is satisfied precisely. However, because these equations only model the physics approximately, this does not mean that the solution exactly matches what happens in reality. If a solution is converging, residuals should decrease with successive timesteps.

For example, assume that a given residual is 0.0005 kg s^-1. It is not obvious whether such a residual is large or small. For instance, if the problem involves flows such that about 0.5 kg flows into (and out of) each mesh element every second, then a residual of 0.0005 kg s^-1 means the equation is satisfied to within one part in a thousand, which is likely a reasonable solution. However, if the problem involves flows of about 0.001 kg s^-1 into each mesh element, then the residual is nearly as large as the flow, and the solution is not good.

To make the scales of the residuals meaningful, the solver normalizes values by dividing the appropriate scales at each point. CFX-Solver Manager plots these normalized residuals using a log (base 10) scale.

The exact details of how the residuals are normalized are involved. For details, see Residual Normalization Procedure in the CFX-Solver Theory Guide. However, it is useful to know that residuals are divided by the solution range. If the linear solution diverges, this range may be very large and the normalized residuals would be meaningless.

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