ON SOME RECENT ADVENTURES INTO IMPROVED FINITE-ELEMENT CFD METHODS FOR CONVECTIVE-TRANSPORT

The quest continues for computational fluid dynamics (CFD) algorithms that are accurate and efficient for convection-dominated applications including shocks, travelling fronts and wall-layers. The boundary-valu e 'optimal' Galerkin weak statement invariably requires manipulation, either in the test space or in an augmented form for the conservation law system, to handle the disruptive character introduced by the discr etized first-order convection term. An incredible variety of methodolo gies have been derived and examined to address this issue, in particul ar seeking achievement of accurate and monotone discrete approximate s olutions in an efficient implementation. The UTK CFD research group co ntinues its search on examining the breadth of approaches leading to d evelopment of a consistent, encompassing theoretical statement exhibit ing quality performance. Included herein are adventures into generaliz ed Taylor series (Lax-Wendroff) methods, characteristic Euler flux res olutions, sub-grid embedded high-degree Lagrange bases with static con densation, and assembled-stencil Fourier analysis optimization for fin ite element weak statement implementations. For appropriate model prob lems, including steady convection-diffusion and pure unsteady convecti on, and benchmark Navier-Stokes definitions, recent advances have lead to candidate accurate monotone methods with linear basis efficiency. This contribution highlights the theoretical developments, and present s quantitative documentation of achievable high quality solutions.