Benefits of Minimal Error Simulation Methods for Turbulent Flows Stefan Heinz ∗ and Adeyemi Fagbade † Department of Mathematics and Statistics, University of Wyoming, Laramie, USA Turbulent flows of practical relevance are often characterized by high Reynolds num- bers 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. Ba- sically, only a few of such methods are regularly applied that are known to suffer from significant shortcomings: such methods are often characterized by significant uncertainty of predictions because of a variety of adjustable simulation settings, their computational cost can be very essential because performance shortcomings need to be compensated by a higher resolution, there are questions about their reliability because the flow resolving ability is unclear, all such predictions require justification. The paper contrasts usually applied simulation methods with minimal error simulation methods presented recently. The comparisons are used to address essential questions about required characteristics of desired simulation methods. The advantages of novel simulation methods (including their simplicity, significant computational cost reductions and a controlled resolution ability) are pointed out. Advantages are reported in regard to periodic hill flow simulations and NASA wall-mounted hump flow simulations. I. Introduction There are significant challenges for computational fluid dynamics (CFD) in regard to the solution of problems of practical relevance. The latter are usually characterized by a high Reynolds number (Re) and complex geometries, which implies flow separation playing a significant role. The problem is that usually applied methods like Reynolds-averaged Navier-Stokes (RANS), large eddy simulation (LES), and hybrid RANS-LES methods suffer for decades from well known problems: RANS can be unreliable because of missing instantaneous turbulence, LES can be unreliable as validation method because of its unclear flow resolution standard, and hybrid RANS-LES can suffer from uncertainty depending on simulation settings and high cost because of uncontrolled resolution. The resulting CFD dilemma is a significant waste of resources, and, first of all, the current inability to reliably predict and study very high Re complex flow problems. In particular, all such existing methods require validation of their results, which is usually hardly possible because experiments cannot be performed at very Re seen in reality. It is worth noting that corresponding issues apply to a variety of other problems, as, for example, mesoscale and microscale modeling in regard to atmospheric simulations 1–3 and many technical applications. 4 The motivation for this paper is to address consequences of this development and ways to overcome such significant problems. The problems and their relevance are specified in Sect. II. Novel simulation methods based on exact mathematics and their implications for usually applied methods are presented in Sect. III. Applications are reported in Sect. IV and Sect. V. Conclusions are presented in Sect. VI. II. The CFD Dilemma To prepare the presentation of minimal error simulation methods in Sect. III, let us consider first typical CFD problems more specifically. 5 * Professor, Associate AIAA Fellow, email: heinz@uwyo.edu, corresponding author. † PhD student, Department of Mathematics and Statistics, University of Wyoming. 1 of 18 American Institute of Aeronautics and Astronautics Downloaded by Stefan Heinz on January 4, 2024 | http://arc.aiaa.org | DOI: 10.2514/6.2024-0293 AIAA SCITECH 2024 Forum 8-12 January 2024, Orlando, FL 10.2514/6.2024-0293 Copyright © 2024 by Stefan Heinz. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. AIAA SciTech Forum