41st NIA CFD Seminar

Topic: The MOOD Method --- Multidimensional Optimal Order Detection -- a first a posteriori approach to Very-High-Order Finite Volumes methods

Date: Tuesday, September 24, 2013

Time:11:00am-noon (EST),

Location: NIA room 101

Speaker: Steven Diot

Biography: Dr. Steven Diot is Postdoctoral Research Associate at the Los Alamos National Laboratory. He received his Ph.D. degree in Applied Mathematics from the University of Toulouse (France) in 2012. During his Ph.D. research studies, he developed a new approach to Very-High-Order Finite Volume methods for single-material compressible flows called the Multidimensional Optimal Order Detection (MOOD) method. An important part of his postdoctoral studies is the extension of the MOOD method to multi-material compressible flows and to coupled physics.

Abstract: This talk will be dedicated to the new type of very high-order Finite Volume methods for hyperbolic systems of conservation laws that I introduced and developed during my doctoral studies. This method, named MOOD for Multidimensional Optimal Order Detection, provides very accurate simulations for two- and three-dimensional unstructured meshes. The design of such a method is made delicate by the emergence of solution singularities (shocks, contact discontinuities) for which spurious phenomena (oscillations, nonphysical values creation, etc.) are generated by the high-order approximation. The originality of this work lies in a new treatment for theses problems. Contrary to classical methods which try to control such undesirable phenomena through an a priori limitation, we propose an a posteriori treatment approach based on a local scheme order decrementing. In particular, we show that this concept easily provides properties that are usually difficult to prove in a multidimensional unstructured framework (positivity-preserving for instance). The robustness and quality of the MOOD method have been numerically proved through numerous test cases in 2D and 3D for single-material compressible flows, and a significant reduction of computational resources (CPU and memory storage) needed to get state-of-the-art results has been shown. I will moreover present some preliminary results on my current work at LANL for the case of multi-material compressible flows.

Additional information, including the webcast link, can be found at the NIA CFD Seminar website, which is temporarily located at

http://www.hiroakinishikawa.com/niacfds/index.html