A Mathematical Solution to the Computational Fluid Dynamics (CFD) Dilemma

Abstract

Turbulent flows of practical relevance are often characterized by high Reynolds numbers and solid boundaries. The need to account for flow separation seen in such flows requires the use of (partially) resolving simulation methods on relatively coarse grids. The development of such computational methods is characterized by stagnation. Basically, only a few methods are regularly applied that are known to suffer from significant shortcomings: such methods are often characterized by the significant uncertainty of the predictions due to a variety of adjustable simulation settings, their computational cost can be essential because performance shortcomings need to be compensated by a higher resolution, and there are questions about their reliability because the flow resolving ability is unclear; hence, all such predictions require justification. A substantial reason for this dilemma is of a conceptual nature: the lack of clarity about the essential questions. The paper contrasts the usually applied simulation methods with the minimal error simulation methods presented recently. The comparisons are used to address essential questions about the required characteristics of the desired simulation methods. The advantages of novel simulation methods (including their simplicity, significant computational cost reductions, and controlled resolution ability) are pointed out.