Impact of source terms on reliability of CFD algorithms

Source terms often appear in various fluid dynamic problems. These source terms not only have an important impact on the physics of the flow but they can also impact the reliability of CFD algorithms. A general recommendation is to treat negative values (sinks) implicitly, while positive values (sources) should be evaluated explicitly. Although this provides improvements compared with evaluating all terms in the same manner, sources with positive values, in particular, often cause code reliability issues. The present paper addresses the reasons for these difficulties and combines a new source term evaluation method with time step limitation for convection and diffusion terms to give more robust capability. The method is verified by a combination of stability analyses followed by computational experiments to validate the stability findings in meaningful problems. The source Jacobian arising from a two-equation k–ω turbulence model is taken as an example to demonstrate our findings.