The Role of Mesh Generation, Adaptation, and Refinement on the Computation of Flows Featuring Strong Shocks

Abstract

Within a continuum framework, flows featuring shock waves can be modelled by means of either shock capturing or shock fitting. Shock-capturing codes are algorithmically simple, but are plagued by a number of numerical troubles, particularly evident when shocks are strong and the grids unstructured. On the other hand, shock-fitting algorithms on structured grids allow to accurately compute solutions on coarse meshes, but tend to be algorithmically complex. We show how recent advances in computational mesh generation allow to relieve some of the difficulties encountered by shock capturing and contribute towards making shock fitting on unstructured meshes a versatile technique.

Numerical study of the flow around spacecraft model

“…В частности, на основании обзора аэродинамических характеристик, измеренных в различных аэродинамических трубах США, Франции, Германии и других стран, в серию эталонных моделей AGARD 1 были включены две геометриче- 1 Advisory Group for Aerospace Research and Development -совещательный комитет при НАТО по научно-исследовательским и опытно-констукторским работам в области авиации и космонавтики ские компоновки гиперзвуковой баллистической модели, представляющей со-бой цилиндр, имеющий носовую часть в виде притупленного конуса с расши-ряющейся хвостовой частью или без нее (НВ-2 и НВ-1 соответственно). Данная задача на примере тел различных конфигураций была подробно исследована экспериментально [3][4][5][6][7][8][9][10][11][12][13][14], теоретически [13][14][15][16] и численно [3,[17][18][19][20][21]. Численные исследования проводились как в рамках уравнений Эйлера, так и Навье-Стокса с различными моделями турбулентности.…”

UQ eSpace

“…The boundary method involves aligning a grid boundary with the shock. The grid deforms as the flow evolves in time and the grid boundary moves with the shock [29]. It is not possible to fit more than one shock or embedded shocks using this method, and it is mostly suited to modeling bow shocks [20,29].…”

“…Although the floating point method can be used to model more complicated flow than the boundary method, including shock interactions [31], it is algorithmically very difficult [29]. It has been suggested that a hybrid fitting-capturing approach can be used in configurations with one main (fitted) shock and subsequent weaker (captured) shocks [3].…”

“…• The front tracking method was chosen instead of the boundary fitting method, as it can be used in a wider variety of test cases including multiple and embedded shocks [29]. Furthermore, much of the numerical implementation in 1D is shared between the methods and hence it is believed that the results in 1D are representative of either method [29].…”

“…The fitting method employed here was a front tracking method as opposed to a boundary fitting method. In higher dimensions this method has been noted as much more complex, so this is something to keep in mind [29,30]. The boundary fitting method is simpler in higher dimensions, however is also limited by the flow problems for which it can be used.…”