### 11.3.2. Controlling Error Propagation

Controlling the transport and, more importantly, the amplification of error, is also critical, given that sources of solution error can often only be reduced and not eliminated. Little can be done to reduce error transport because error is subject to the same physical processes (such as, advection or diffusion) as the conserved quantities. Fortunately, the amplification of error is more easily controlled.

Errors are amplified by strong unphysical influences in the discrete form of the modeled equations. These unphysical influences will lead to convergence difficulties, and in extreme cases, complete divergence. Similar to error sources, error amplification is controlled through the choice of discretization and/or the mesh distribution.

As highlighted above, (unphysical) negative influences may be introduced into the discretization through the finite-element shape functions, and these influences may grow as geometrical mesh quality (see Measures of Mesh Quality in the CFX-Solver Modeling Guide) deteriorates. Tri-linear shape functions, for example, are more susceptible to negative influences than linear-linear shape functions. Nevertheless, tri-linear shape functions are used as much as possible due to their improved accuracy, and linear-linear shape functions are used whenever solution robustness is critical.

Geometrical mesh quality is important regardless of the shape functions used. An excellent example of this occurs when mesh elements are folded. If the mesh is sufficiently folded, control volumes become negative and the balance between the transient/storage and flow terms is rendered physically invalid. The amount of a conserved quantity within a control volume will actually decrease given a net flow into the control volume.

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