Multi-Dimensional Upwind Fluctuation Splitting Scheme With Mesh Adaption for Hypersonic Viscous Flow

<p>A multi-dimensional upwind fluctuation splitting scheme is developed and implemented for two-dimensional and axisymmetric formulations of the Navier-Stokes equations on unstructured meshes. Key features of the scheme are the compact stencil full upwinding and non-linear discretization which allow for second-order accuracy with enforced positivity. Throughout the fluctuation splitting scheme is compared to a current state-of-the-art finite volume approach a second-order dual mesh upwind flux difference splitting scheme (DMFDSFV) and is shown to produce more accurate results using fewer computer resources for a wide range of test cases. A Blasius flat plate viscous validation case reveals a more accurate upsilon-velocity profile for fluctuation splitting and the reduced artificial dissipation production is shown relative to DMFDSFV. Remarkably the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. The second half of the report develops a local compact anisotropic unstructured mesh adaptation scheme in conjunction with the multi-dimensional upwind solver exhibiting a characteristic alignment behavior for scalar problems. The adaptation strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization.</p><p>This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact and remains as true to the original work as possible. Therefore you will see the original copyright references library stamps (as most of these works have been housed in our most important libraries around the world) and other notations in the work.</p><p>This work is in the public domain in the United States of America and possibly other nations. Within the United States you may freely copy and distribute this work as no entity (individual or corporate) has a copyright on the body of the work.</p><p>As a reproduction of a historical artifact this work may contain missing or blurred pages poor pictures errant marks etc. Scholars believe and we concur that this work is important enough to be preserved reproduced and made generally available to the public. We appreciate your support of the preservation process and thank you for being an important part of keeping this knowledge alive and relevant.</p>