A compact high-order unstructured grids method for the solution of Euler equations

Demonstration of ultra hi-fi (UHF) methods

“…The extension to Euler equations is laid out in (ref. 6) for unstructured single cell reconstruction and a demonstration of the multiblock structured two-cell reconstruction is being prepared. Space limitations preclude explaining more.…”

“…In a similar vein, UHF methods use Cauchy-Kowalewski-Taylor time advance, and the spatial derivatives of the cell averages are carried on the grid; And Hermite fluxes are calculated and used to conservatively time advance all derivatives of the cell averages (ref. 6). This can be formulated with unstructured grids with upwinding (ref.…”

“…If an unstaggered single cell reconstruction is used as in (ref. 6), then an upwinding dissipation term should be included for stability.…”

Review of Computational Stirling Analysis Methods

“…The a i,j coefficients can be found using Hermitian divided differences 51 As was done by Agarwal 59 and similar to Goodrich 70 the governing equations may be differentiated as follows in curvilinear coordinates:…”

On Obtaining High-Order Finite-Volume Solutions to the Euler Equations on Unstructured Meshes

“…Since Barth and Frederickson's pioneering work, 1 a number of researchers have studied high-order (by which we mean third-and fourth-order accurate) finite-volume methods for computational aerodynamics using unstructured meshes [2][3][4][5][6][7][8][9] For the most part, however, these researchers tend to content themselves primarily with showing that highorder schemes are superior in accuracy to second-order schemes without quantifying the order of accuracy of their scheme. Some of the research described in the literature also explicitly fails to implement all terms to high-order accuracy.…”