By Wai-How Hui, Kun Xu
Derivation of Conservation legislations Equations.- evaluate of Eulerian Computation for One-dimensional Flow.- One-Dimensional circulate Computation utilizing the Unified Coordinates.- reviews on present tools for Multi-Dimensional circulation Computation.- The Unified Coordinates formula of CFD.- houses of the Unified Coordinates.- Lagrangian fuel Dynamics.- regular 2-D and 3D Supersonic Flow.- Unsteady 2-D and three-D movement Computation.- Viscous circulation Computation.- functions of the Unified Coordinates to Kinetic concept
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Additional resources for Computational Fluid Dynamics Based on the Unified Coordinates
Hafez, K. Morinishi, and J. Periaux (Eds), 309-321, 2001.  K. L. Mao and L. Tang. A multidimensional gas-kinetic BGK scheme for hypersonic viscous ﬂow. J. Comput. , 203: 405-421, 2005.  J. Quirk. A contribution to the great Riemann solver debate. Int. J. Num. Met. Fluids, 18: 555-574, 1994. J. LeVeque. Nonlinear conservation laws and ﬁnite volume methods for astrophysical ﬂuid ﬂow. Computational Methods for Astrophysical Flow, Edited by O. Steiner and A. Gautschy, New York: Springer-Verlag, 1998.
37) 1 a ρ ⎞ ⎟ ⎟ ⎟. 38) a2 wave. On the other hand, both λ1 -ﬁeld and λ3 -ﬁeld are genuinely non-linear, each of which giving rise to a shock or a rarefaction wave. (1) The λ2 -ﬁeld. 39) but there is no relation between ρ2 and ρ3 . (2) The λ1 -ﬁeld. Case 1: p2 > p . 3) a shock wave can pressure of a particle increases; it cannot do so on crossing a rarefaction wave. We also pointed out earlier that as pressure increases crossing a shock, so does entropy of the ﬂuid particle. So we 30 Chapter 3 Review of Eulerian Computation for 1-D Inviscid Flow have implicitly applied the entropy condition at this stage.
Certainly, if the shock discontinuity or slip surface can be well resolved by shock or contact ﬁtting methods, the additional dissipation can be avoided (see Chapter 4). The use of the Riemann solution somehow helps to introduces the “appropriate” numerical dissipation needed in the discontinuity region. However, contrary to many statements in the literatures, the amount of dissipation in the Godunov method is not coming from the characteristic waves of the Riemann solution or the so-called upwinding mechanism, but is coming from the preparation of the initial data at the beginning of each time.