AFRL-AFOSR-VA-TR-2015-0289 Hybridized Multiscale Discontinuous Galerkin Methods for Multiphysics

We have continued the development of the Hybridized Discontinuous Galerkin(HDG) method for the solution of systems of conservation laws. The focus hasbeen on the development of robust, accurate, and efficient methods capable ofhandling complex physics in realistic geometries. In particular, we have: 1)proposed a Hybridized Multiscale Discontinuous Galerkin method (HMDG)which allow us to freely modify the local approximations spaces on eachsubdomain, 2) introduced hybridization and postprocessing techniques for theHDG approximation of second-order elliptic eigenvalue problems, 3) presented anew class of HDG methods capable of generating high-quality approximations ofthe Helmholtz equation for a very wide range of wave frequencies, 4) presentedan embedded discontinuous Galerkin (EDG) method for numerically solving theEuler equations and the Navier-Stokes equations, 5) introduced a novel shock DISTRIBUTION A: Distribution approved for public release. 9/8/15, 12:40 PMAFOSR Deliverables Submission Survey Page 2 of 2file:///Users/peraire/Dropbox%20(MIT)/DATA/AFOSR%20Grants/AF...eport%202015/AFOSR%20Deliverables%20Submission%20Survey.htmlcapturing artificial viscosity technique for high-order unstructured mesh methods,6) introduced an explicit hybridizable discontinuous Galerkin (HDG) method forthe acoustic wave equation, and finally, 7) presented a new statistical approach tothe problem of incorporating experimental observations into a mathematicalmodel described by linear partial differential equations (PDEs) to improve theprediction of the state of a physical system. We have also illustrated our methodson number of applications in fluid mechanics and electromagnetics.DistributionStatement: Distribution A Approved for Public ReleaseSF298 Form: 184-ee57cf3760b82c8573b34f370403d58e_Peraire_SF298.pdfReportDocument 36-e60b249ab1d323f9241e3e08d9d910c2_AFOSR-HDG2015-Report.pdfArchivalPublications: Listed in ReportChanges inResearchobjectives:None Change inAFOSRProgramManager, ifany:Original Program Manager: Dr. Fariba Fahroo Current Program Manager: Jean-Luc Cambier Extensionsgranted ormilestonesslipped, if any:None