Open boundaries

Sani, R. L. and Gresho, P. M., 1994. Resume and remarks on the Open Boundary Condition Mini-symposium, Int. J. Numer. Fluids 18, 983-1008,... 

Comparison of Solutions of Continuity Equation for DPF. The results for the three cases discussed above, together with those for the case with closed-open boundary conditions, are summarized in Table 19.7. Included in Table 19.7 are the boundary conditions, the expression for C(0) at z = 1, and the mean and variance of C(0). For large values of PeL, the solutions are not very different, but for small values, the results differ considerably. 

One conclusion from these results is that the axial diffusion model begins to fail as Pe, - small, when an open boundary condition is used at the outlet. The case Pe, - small means increasing backmixing, or that the diffusive flux becomes increasingly significant compared with the convective flux. For an open boundary condition, it is also questionable whether the actual response C(e) can be identified with E(B). Furthermore, regardless of the boundary conditions chosen, it is difficult to envisage that cA... 

New computational approaches are developed to explore flame stabilization techniques in subsonic ramjets. The primary focus is statistical modeling of turbulent combustion and derivation of the adequate boundary conditions at open boundaries. The mechanism of flame stabilization and blow-off in ramjet burners is discussed. The criterion of flame stability based on the clearly defined characteristic residence and reaction times is suggested and validated by numerical simulations. 

The results of numerical simulation of bluff-body stabilized premixed flames by the PPDF method are presented in section 12.2. This method was developed to conduct parametric studies before applying a more sophisticated and CPU time consuming PC JVS PDF method. The adequate boundary conditions (ABC) at open boundaries derived in section 12.3 play an essential role in the analysis. Section 12.4 deals with testing and validating the computational method and discussing the mechanism of flame stabilization and blow-off. 

Application of ABC of Eqs. (12.19), (12.23), and (12.25), on the one side, and standard Dirichlet or von Neumann boundary conditions at open boundaries, on the other side, reveals the drastic effect of outlet boundary conditions on the flow pattern. 

The Presumed Probability Density Function method is developed and implemented to study turbulent flame stabilization and combustion control in subsonic combustors with flame holders. The method considers turbulence-chemistry interaction, multiple thermo-chemical variables, variable pressure, near-wall effects, and provides the efficient research tool for studying flame stabilization and blow-off in practical ramjet burners. Nonreflecting multidimensional boundary conditions at open boundaries are derived, and implemented into the current research. The boundary conditions provide transparency to acoustic waves generated in bluff-body stabilized combustion zones, thus avoiding numerically induced oscillations and instabilities. It is shown that predicted flow patterns in a combustor are essentially affected by the boundary conditions. The derived nonreflecting boundary conditions provide the solutions corresponding to experimental findings. 

Grinstein, F. 1994. Open boundary conditions in the simulation of subsonic turbulent shear flows. J. Compt. Physics 115(1) 43. 

The numerical jet model [9-11] is based on the numerical solution of the time-dependent, compressible flow conservation equations for total mass, energy, momentum, and chemical species number densities, with appropriate in-flow/outfiow open-boundary conditions and an ideal gas equation of state. In the reactive simulations, multispecies temperature-dependent diffusion and thermal conduction processes [11, 12] are calculated explicitly using central difference approximations and coupled to chemical kinetics and convection using timestep-splitting techniques [13]. Global models for hydrogen [14] and propane chemistry [15] have been used in the 3D, time-dependent reactive jet simulations. Extensive comparisons with laboratory experiments have been reported for non-reactive jets [9, 16] validation of the reactive/diffusive models is discussed in [14]. 

In all cases you can evaluate D/wL from the parameters of the tracer curves however, each curve has its own mathematics. Let us look at the tracer curves for closed and for the open boundary conditions. 

We will not discuss the equations and curves for the open-closed or closed-open boundary conditions. These can be found in Levenspiel (1996). 

G.H. Evans and S. Paolucci. The Thermoconvective Instability of Plane Poiseuille Flow Heated from Below A Proposed Benchmark Solution for Open Boundary Flows. Int. J. Num. Meth. Fluids, 11 1001-1013,1990. 

To calculate the electronic states of such devices, two problems should be solved. First, the infinitely large problem (due to the electrodes) must be reduced to a finite one which is manageable on a computer. This means that one has to solve an open boundary problem. Second, within DFT, one needs to find charge density p(r) of the molecule and electrodes under a bias voltage across the open device. We will assume that rl it is not... 

By the middle 2000s, the model used [42] had been physically and numerically enhanced by the introduction of biharmonic horizontal mixing of the momentum, free sea surface, and actual thermodynamic fluxes at all the open boundaries implemented with a 15-km horizontal resolution, 44 levels over the vertical and a 5-min time step [44,45]. In the latter papers, instead of the density fields [9], climatic temperature and salinity fields with a twice coarser horizontal resolution (about 37 km) were used based on a twofold greater database (about 100 000 stations). 

A surface is closed if it has no boundary curves. By this definition surfaces of a sphere and a torus are closed, whilst the surfaces of a hollow cylinder and of a disc are open. Boundary curves of two-sided surfaces are curves which separate one side of the surface from the other, for example the edges of a piece of thin paper. A completely open cylinder has two boundary curves. A cylinder which is half-open has only one boundary curve, and is continuously deformable into, and therefore topologically equivalent to a disc. Similarly, the removal of a disc from the surface of a sphere leaves an... 

M. Renardy, Existence of steady flows for Maxwell fluids with traction boundary conditions on open boundaries, Z. Angew. Math. Mech. 75 (1995) 153-155. 

Arndt N. T. and Goldstein S. L. (1989) An open boundary between lower continental crust and mantle its role in crust formation and crustal recycling. Tectonophysics 161, 201-212. 

Drums, barrels, carboys and other similar containers for fast pyrolysis liquid should be stored in the external air on an inq ervious and durable surface, which is in excess of 4 m to any risk area, bund or open boundary. The area should be protected by a bund wall, dished or ramped to contain spillages, with the walls and floor impervious to the materials stored. The bunded area should contain no drains or valves. Vehicular access to such areas should be protected by a ramp or a channel ensuring that the ramp itself does not cause regular spillages. 

Fig. 21 Plots obtained by mean-field calculations for an EHFMI [24]. Calculations are performed for a two-dimensional 16x16 square lattice with open boundary conditions. Parameters used are U = St and t = —0.2t t denotes the second nearest neighbor transfer integrals tjk)- The number of doped holes is 8 half of them are centers of merons and the rest are centers of antimerons. (a) Plot for spin configuration. Centers of spin vortices are indicated as M for a meron (winding number -H spin vortex) and A for an antimeron (winding number —1 spin vortex), respectively, (b) Plot for current density j (short black arrows) and V x (long orange arrows). M and A here indicate centers of counterclockwise and clockwise loop currents, respectively (c) Plot for D(x), which connects j(x) and V/(x) as j(x) = D(x) V/(x) (d) Plot for 2j (thick orange line arrows are not attached but directions are the same as those of the black arrows) and 2Z)(x) V/(x) (black arrows)...

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