A global approach to error estimation and physical diagnostics in multidimensional computational fluid dynamics

Abstract

AbstractAn approach for simultaneously assessing numerical accuracy and extracting physical information from multidimensional calculations of complex (engineering) flows is proposed and demonstrated. The method is based on global balance equations, i.e. volume‐integrated partial differential equations for primary or derived physical quantities of interest. Balances can be applied to the full computational domain or to any subdomain down to the single‐cell level. Applications to in‐cylinder flows in reciprocating engines are used for illustration. It is demonstrated that comparison of the relative magnitude of the terms in the balances provides insight into the physics of the flow being computed. Moreover, for quantities that are not conserved at the cell or control volume level in the construction of the numerical scheme, the imbalance allows a direct assessment of numerical accuracy in a single run using a single mesh. The mean kinetic energy imbalance is shown to be a particularly sensitive indicator of numerical accuracy. This simple and powerful diagnostic approach can be implemented for finite‐difference, finite‐volume or finite‐element methods.