By Wai-How Hui, Kun Xu
Derivation of Conservation legislation Equations.- overview of Eulerian Computation for One-dimensional Flow.- One-Dimensional move Computation utilizing the Unified Coordinates.- reviews on present tools for Multi-Dimensional circulate Computation.- The Unified Coordinates formula of CFD.- homes of the Unified Coordinates.- Lagrangian fuel Dynamics.- regular 2-D and 3-D Supersonic Flow.- Unsteady 2-D and three-D circulation Computation.- Viscous circulate Computation.- functions of the Unified Coordinates to Kinetic idea
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Additional resources for Computational Fluid Dynamics Based on the Unified Coordinates
6) ⎛ ⎞ (u − U )ρu ⎜ (u − U )ρu2 + p ⎟ ⎟ F =⎜ ⎝ (u − U )ρue + up ⎠ . 4) for dx. 3) are also in conservation PDE form. 3) in λ-direction. 6) is also hyperbolic in λ-direction, despite the fact that the transformation involves the unknown function v. 7) 1/2 is the speed of sound. 8) T . 6) is hyperbolic in λ-direction. 1), both hyperbolic and in conservation form, these systems can be solved similarly to the Eulerian one. In particular, any shock-capturing methods developed for conservation laws (as summarized in Chapter 3) apply.
It reproduces the exact analytic solution, as predicted. 2 Slow moving shock In computing an isolated shock, if the shock is slow-moving the disturbances due to the shock is of low frequencies (long waves). The numerical dissipation near the shock is small for slow-moving shocks and may not be suﬃcient to damp the long waves down. 0. 11. In the Lagrangian coordinates the speed of a shock wave is always greater (in magnitude) than the characteristic speed, aρ, and hence the shock cannot be slowmoving.
1) where e= 1 p 1 2 u + . 1) become ⎛ ⎛ ⎞ ⎞ 1/ρ −u ∂ ⎝ ∂ ⎝ p ⎠ = 0. 3) is seen to be in conservation PDE form. 4) where U (λ, ξ) is an arbitrary function. It can easily be shown that ∂ξ ∂ξ +U = 0. H. 5) 44 Chapter 4 1-D Flow Computation Using the Uniﬁed Coordinates This means that the coordinate ξ is invariant following a pseudo-particle whose velocity is U . Consequently, computational cells move with the pseudo-particles, instead of the ﬂuid particles as in Lagrangian coordinates. As we can see from the above transformation, the case U = 0 gives us the Eulerian coordinates in which ξ is independent of the ﬂow; in particular, ξ = x if A = 1.
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