Thursday, January 15,  in ETRL 101 from 11 a.m. to noon
Refreshments served in ETRL 119 at 10:30 a.m.

Dr. Tao Xing, Ph.D., P.E.
Associate Professor, Department of Mechanical Engineering
University of Idaho, Moscow, Idaho

Solution Verification for Large Eddy Simulations In Computational Fluid Dynamics


With the dramatic growth of supercomputers, simulation based design, and ultimately virtual reality, have become increasingly important for the advancement of science and engineering.  Computational fluid dynamics (CFD) provides   computerized solutions for science and engineering problems using modeling, numerical methods, and high-performance computing. In CFD, the continuous partial differential equations are discretized into algebraic equations using numerical methods.  The algebraic equations are assembled and solved to get approximate solutions.  Thus, it is imperative to quantitatively estimate the numerical and modeling errors and associated uncertainties, which can only be achieved through rigorous verification and validation (V&V).  Additionally, guidelines for how to optimize a CFD simulation to obtain a minimum total simulation error are needed.  In this speech, definitions, general methodology and procedures of V&V will be covered. Based on statistical analysis, the “Factor of Safety” method shows advantages over various versions of the grid convergence index method, correction factor method, and least square method for Reynolds-averaged   Navier-Stokes (RANS) V&V.  Nonetheless, these methods cannot be applied directly to large eddy simulations (LES) V&V.  Recently, a general framework for LES V&V was developed including a vast number methods based on two Hypotheses, ranging from a sophisticated seven-equation method to a simple single grid method. These methods were evaluated using implicitly filtered LES of periodic channel flows at friction Reynolds number of 395 on eight systematically refined grids. The seven-equation method shows that the coupling error based on Hypothesis I is much smaller as compared to the numerical and modeling errors and therefore can be neglected. The five-equation method based on Hypothesis II is recommended, which shows a monotonic convergence behavior of the predicted numerical benchmark (SC), and provides realistic error estimates without the need of fixing the orders of accuracy for either numerical or modeling errors. Based on the results from seven-equation and five-equation methods, less expensive three and four-equation methods for practical LES applications were derived. It was found that the new three-equation method is robust as it can be applied to any convergence types and reasonably predicts the error trends. It was also observed that the numerical and modeling errors usually have opposite signs in LES, which suggests error cancellation play an essential role in LES. When RANS verification method is applied, it shows significant error in the prediction of SC on coarse meshes. However, it predicts reasonable SC when the grids resolve at least 80% of the total turbulent kinetic energy.


Dr. Tao Xing earned his Ph.D. in Mechanical Engineering from Purdue University in 2002. He worked as a Postdoctoral    Fellow and Assistant Research Scientist at the Iowa Institute of Hydraulics Research from 2002 to 2008. He was an Assistant Professor from 2009 to 2016. Dr. Xing is currently an Associate Professor at University of Idaho. His research interests focus on both fundamental and applied CFD in multi-disciplines. Fundamental CFD research includes estimation of errors and uncertainties using quantitate solution verification and validation (V&V) method for turbulent flow simulations and entropy generation for bypass transitional boundary layers. For V&V, the “factor of safety method” he developed was evaluated as the most accurate and concise uncertainty estimates for monotonically converged numerical solutions.  He was invited to give 12 lectures including the keynote lecture on verification and validation in the 13th National Congress on Hydrodynamics in China in 2014. In 2015, he developed a general framework for V&V for large eddy simulations and very recently five-equation and robust   three-equation methods for LES V&V. Applied CFD research covers a broad range of disciplines including onshore and offshore wind turbine designs, vehicle aerodynamics, fluid-structure interaction for pulmonary ventilation, ship hydrodynamics, and desalination. Dr. Xing’s teaching interests focus on integration of simulation technology into engineering courses and laboratories, development of effective formative and summative evaluation   methods, and development of innovative teaching modules toward achieving ABET learning outcomes. His Google Scholar h-index and i10-index are 19 and 29, respectively. As a PI or Co-PI, he secured more than 1.8 million dollars funding since he joined the University of Idaho in 2011. He won the “Alumni Award” from the University of Idaho in 2013 and again in 2014. He won the “Outstanding Young Faculty Award” from College of Engineering in 2015. He is a licensed U.S. Professional Engineer.