Numerical Examination of Flux Correction for Solving the Navier-Stokes Equations on Unstructured Meshes.

摘要

This work examines the feasibility of a novel high-order numerical method, which has been termed Flux Correction. This is accomplished by comparing it against another high-order method called Flux Reconstruction. These numerical methods are used to solve the Navier-Stokes equations, which govern the motion of fluid flow. High-order numerical methods, or those that demonstrate a third-order and higher solution error convergence rate, are rarely used on unstructured meshes when solving fluid problems. Flux Correction intends to make high-order accuracy available to the larger world of Computational Fluid Dynamics in a simple and effective manner. The advantages and disadvantages of the method can only be discovered when compared against other high-order numerical methods. This work accomplishes this by comparing Flux Correction and Flux Reconstruction in terms of accuracy, numerical dissipation, and solution times. Flux Correction is found to compare favorably in terms of accuracy, and exceed expectations for convergence rates. Flux Correction is also tested on high-order meshes, or meshes that use high-order polynomials in the construction of the unstructured triangle mesh. High-order meshes generate long, thin elements, which are found to negatively impact the convergence and accuracy of Flux Correction.