Artificial viscosity proper orthogonal decomposition

• Published in: Mathematical and computer modelling Vol. 53; no. 1; pp. 269 - 279
• Main Authors: Borggaard, Jeff, Iliescu, Traian, Wang, Zhu
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 2011; Elsevier
• Subjects: Artificial viscosity; equations; Exact sciences and technology; Large eddy simulation; Mathematical analysis; Mathematics; methodology; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis; Numerical analysis in abstract spaces; Numerical analysis. Scientific computation; Partial differential equations; Proper orthogonal decomposition; Sciences and techniques of general use; turbulent flow; viscosity; Proper orthogonal decomposition; Artificial viscosity; Large eddy simulation; Viscosity; Turbulence; Turbulent flow; Decomposition method; Burgers equation; Discretization method; Numerical analysis; Applied mathematics; Diffusion equation; Galerkin method; Abstract space; Mathematical model; Computer aided analysis
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2010.08.015

We introduce improved reduced-order models for turbulent flows. These models are inspired from successful methodologies used in large eddy simulation, such as artificial viscosity, applied to standard models created by proper orthogonal decomposition of flows coupled with Galerkin projection. As a first step in the analysis and testing of our new methodology, we use the Burgers equation with a small diffusion parameter. We present a thorough numerical analysis for the time discretization of the new models. We then test these models in two problems displaying shock-like phenomena. Of course, since the Burgers equation does not model turbulence, we next need to test our new models in realistic turbulent flow settings. This is the subject of a forthcoming report.