Investigation of the cese framework for viscous flows

A transient viscous solver has been developed based on the novel space-time conservation element solution element (CESE) framework. Till date, the numerical accuracy of the CESE framework in modeling inviscid flow problems has been well documented, while very little work has been done in regards to modeling transient viscous flows. In this work, an attempt to fill that gap in literature was carried out by rigorously investigating the numerical accuracy and computational performance of the CESE framework in simulating such flows. The study aims at gaining a deeper understanding on the numerical accuracy and dissipation characteristics of the CESE framework, as well as its robustness in handling practical problems of interest. There are four major sections in this work. The first section details the fundamentals of the CESE framework, various schemes available under the framework, and a step-by-step procedure involved in constructing a Navier-Stokes solver using the framework. The second section deals with implementation of boundary conditions, with particular focus on non-slip walls -- a key component of viscous solvers. The treatment of various boundary conditions is explored so that it is consistent with the fundamental aspect of the CESE framework - space-time flux conservation. Two different approaches to model the viscous wall effect have been explored and presented in detail. The third section of this work investigates and assesses: (1) numerical accuracy, dissipation/dispersion characteristics of various schemes in the CESE - framework, (2) influence of grid topology on the accuracy of viscous flow simulation results, and (3) robustness of the developed solver. Viscous flow problems under several categories, which include aeroacoustics and hypersonic flows, are employed to assess those. Furthermore, the use of triangular and tetrahedral meshes for 2-D and 3-D viscous flow simulations respectively, is shown to be more accurate than their structured mesh counterpart under this novel framework. The original CESE framework is 2nd order accurate in both space and time. A higher-order extension to it is proposed and explored in the final section, so that it can be used to solve problems such as computational aeroacoustics, which require high numerical accuracy, without needing a very fine mesh.;Keywords: CFD, numerical-methods, CESE, high-resolution schemes...