Download e-book for iPad: Computational Fluid Dynamics Based on the Unified by Wai-How Hui, Kun Xu
By Wai-How Hui, Kun Xu
Derivation of Conservation legislations Equations.- assessment 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 gasoline Dynamics.- regular 2-D and 3D Supersonic Flow.- Unsteady 2-D and 3-D stream Computation.- Viscous circulation Computation.- purposes of the Unified Coordinates to Kinetic idea
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Extra info for Computational Fluid Dynamics Based on the Unified Coordinates
The presence of a new shock is tested at all cell interfaces. If the splitting criterion is satisﬁed, a new partition is introduced to account for the incoming shock and the cell is split. Step 3: determination of the step size Δλn . 23) for the shock-subcells which represents the intersection point of the ± waves in the shock-subcell, or equivalently, the intersection point of the incoming elementary wave with the opposing cell interface, also an elementary wave. n For an elementary rarefaction wave, σi±1/2 is replaced by the speed of the n leading Mach line (fastest characteristic).
This can be studied similarly to the λ1 -ﬁeld. Case 1: p3 > pr . This results in a shock and we have ⎧ γ−1 ⎪ α+ ⎪ ⎪ ρ3 p3 ⎪ γ+1 ⎪ ⎪ , α= , = ⎪ γ −1 ⎪ ρ pr r ⎪ ⎪ α+1 ⎨ γ +1 γ+1 γ−1 2(α − 1)ar ⎪ ⎪ α+ , u3 = ur − ⎪ ⎪ (γ + 1)α + γ − 1 2γ 2γ ⎪ ⎪ ⎪ ⎪ ⎪ γ+1 γ−1 ⎪ ⎩ s = u r + ar α+ . 53) Again, as the shock strength tends to zero, the pressure ratio α = p3 /pr tends to unity and the shock speed s approaches the characteristic speed λ3 = ur + ar . Case 2: p3 pr . This results in a rarefaction wave, of which the solution is ⎧ 1/γ ⎪ ρ p ⎪ ⎪ = , ⎪ ⎪ ρr pr ⎪ ⎪ ⎪ ⎨ (γ−1)/2γ 2ar p 1 − , u = u + r ⎪ γ−1 pr ⎪ ⎪ ⎪ ⎪ (γ−1)/2γ ⎪ ⎪ p ξ γ − 1 ur 2 ⎪ ⎩ − = + .
E = E(ξ), ξ= x . 24) yields (A − ξI) dE = 0. 24) may possibly be continuous or be discontinuous. 27). 3 Riemann Problem and its Solution 27 dE dE = 0 or = 0. dξ dξ dE (1) = 0. This gives a constant solution dξ E x = const.. 29) dE ⎪ = Cr (i) (E), C = const.. ⎩ dξ (2) The solution is called a centered rarefaction wave. Discontinuous solutions of conservation law, as mentioned in last subsection, include a shock wave and a contact wave. (1) Shock wave. 30) dx is the speed of the shock wave. dt (2) Contact wave.
Computational Fluid Dynamics Based on the Unified Coordinates by Wai-How Hui, Kun Xu