Accession Number : ADA624182


Title :   Application of Parallel Time-Implicit Discontinuous Galerkin Finite Element Methods to Hypersonic Nonequilibrium Flow Problems


Descriptive Note : Doctoral thesis


Corporate Author : FLORIDA UNIV GAINESVILLE DEPT OF MECHANICAL AND AEROSPACE ENGINEERING


Personal Author(s) : Bhatia, Ankush


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a624182.pdf


Report Date : May 2014


Pagination or Media Count : 194


Abstract : Discontinuous Galerkin (DG) methods are high-order accurate, compact-stencil methods, proven to possess favorable properties for highly efficient parallel systems complex geometries and unstructured meshes. Coding effort is significantly reduced for compact-stencil DG methods in comparison to main stream finite difference and finite volume methods. This work successfully introduces DG methods to thermal ablation and non-equilibrium hypersonic flows. In the state-of-the-art hypersonic flow codes, surface heating predictions are very sensitive to mesh resolution in the shock. A minor misalignment can cause major changes in the heating predictions. This is due to the lack of high-order accuracy in current streamline methods and numerical errors associated with the shock capturing approach. Shock capturing methods like slope limiter or artificial viscosity, being empirical have errors in the shock region. This work employs r-p adaptivity to accurately capture the shock with p = 0 elements (first order accuracy). Smooth flow regions are captured using p greater than 0. This method is stable. Implicit methods are developed for solution advancement with high CFL numbers. Error in the shock is reduced by redistributing the elements (outside of the shock) to within the shock (r adaptivity). Inviscid and viscous hypersonic flow problems, with same accuracy as in h-p adaptivity method, are simulated with one-third elements. This methodology requires no a priori knowledge of the shock's location, and is suitable for detached shock problems. r-p adaptivity method has allowed for successful prediction of surface heating rate for hypersonic flow over cylinder. Additionally, good comparisons are made, for non-equilibrium hypersonic flows, to the published results.


Descriptors :   *FINITE ELEMENT ANALYSIS , *GALERKIN METHOD , *HYPERSONIC FLOW , ABLATION , ACCURACY , CODING , COMPARISON , CYLINDRICAL BODIES , ERRORS , HEATING , INVISCID FLOW , LIMITERS , MESH , METHODOLOGY , MISALIGNMENT , NONEQUILIBRIUM FLOW , NUMBERS , NUMERICAL ANALYSIS , PREDICTIONS , RATES , REDUCTION , REGIONS , RESOLUTION , SENSITIVITY , SHOCK , SIMULATION , SLOPE , SOLUTIONS(GENERAL) , STATE OF THE ART , STREAMS , SURFACE TEMPERATURE , THERMAL PROPERTIES , THESES , TOOLS , VISCOSITY , VISCOUS FLOW , VOLUME


Subject Categories : Numerical Mathematics
      Fluid Mechanics


Distribution Statement : APPROVED FOR PUBLIC RELEASE