Open boundary condition

3 Open Boundary Conditions The regional Baltic Sea model has a western open boundary in the Skagerrak. At open boundaries, the model equations for the calculation of horizontal gradients are not complete and boundary conditions are needed to close the numerical scheme. The open boundary conditions implemented in the Baltic Sea version of MOM-3.1 have the following three main components  

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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... 

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). 

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)...

A closed-form solution of Eq. 6.24 has been derived by Lapidus and Amundson [3], Levenspiel and Smith [17], Carberry and Bretton [18], Reilley et al. [19], and Wicke [20]. All these authors used an "open-open" boundary condition, i.e., conditions assuming that the column stretches to infinity in both directions (z —00, dC/dz = 0 z oo, dC/dz = 0), and that a Dirac 6 z) pulse of solute is injected at z = 0. With these boundary conditions, the solution of Eq. 6.24 is given by... 

When the boundary condition is a Dirac S t) function at z = 0 [which is different from the Dirac S z) pulse at z = 0 of the open-open boundary condition], the solution obtained is different. It can be derived using the inverse Laplace transform [21,22] ... 

Cd (pulse boundary condition) = — (open------open boundary condition) (6.32)... 

Figure 6.2 Comparison of the chromatogram given by the equilibrium-dispersive model of chromatography with a Gaussian profile. Dimensionless plot of = Ctn/Ap versus frf = f/tj . Solid line Gaussian profile with N theoretical plates. Dotted line equilibrium-dispersive model with an "open-open" boundary condition and (2D )-...

From the mathematical viewpoint, this solution is quite different, from the solutions obtained with the open-open boundary conditions, although in the latter case we do not make use of the part of the column for which < 0. 

Stevens, D. P., 1990. On open boundary conditions for three dimensional primitive equation ocean circulation models. Geophysical and Astrophysical Fluid, Dynamics, 51, 103-133. 

Laminar Flow between flat plates with radial and axial diffusion Open boundary conditions... 

We note that the Green s function leads to an infinite interaction range. Using open boundary conditions with respect to the computational grid, the stress release from a slipping cell is not conserved on the grid, but on the (infinite) fault plane. 

In the first example shown in Table 9.2, a warm (25°C) water from the ocean s surface (1 atm) has been modeled. In the zone near the equator, where this water sample had been taken, carbon dioxide partial pressures of 400 patm (equivalent to a pCO of 0.0004 atm or a log pCO of -3.40) have been measured which is somewhat higher than the corresponding atmospheric value. This sample of ocean water thus displays a CQ -gradient directed towards the atmosphere and therefore continually releases CQ into the atmosphere. This situation is accounted for in the model by pre-setting pCO to 0.0004 atm as an open boundary condition with regard to CQ. Accordingly, a state of supersaturation ensues equivalent to a SI, , value of 0.77 or an f2, , value of 5.9. Such a supersaturation state is, according to the... 

Determine the conversion predicted using the longitudinal dispersion model. Use open-open boundary conditions. 

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