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3.5.2 Physical and Numerical Specifications
ОглавлениеOnce geometrical definition and meshing are done, simulation models are set up with various input specifications (i.e. Steps 3 and 4 in Table 1). Those associated with Step 3 are physical; that is, they describe the physical characteristics of the process, which in turn affect the degree to which field variables at neighboring grid cells (or mesh nodes) influence each other. Essential are material specifications and associated properties, such as viscosity (for fluids), thermal conductivity, density, specific heat, etc. Many software products have material properties defined for commonly used materials, which must be complemented for materials of interest not dealt with in the existing material database. Various boundary conditions such as flow rates, temperatures, and other state parameters at all flow inlets are other physical specifications to be included along with wall boundaries conditions, which could be, for example, a prescribed temperature, heat flux, or temperature‐dependent heat flux.
Every portion of the boundary of the simulation domain requires a boundary condition for each transport equation considered. These conditions can be in the form of a prescribed field variable (e.g. temperature T), prescribed flux by definition proportional to the gradient of the field variable , or a mixed condition where the flux depends on the field variable (e.g. q ″ = h(T − Tc)). Software products generally provide default values for many of these but, for best practice, much care is recommended to review and verify each boundary condition specification with a checklist. Experience has shown that unintended specifications can be the root cause of the frustrating experience of trying to resolve inconsistencies between simulation results and measured data and/or expectations.
In Table 1, model set up specifications for Step 4 are related to the numerical methodologies employed to render a solution. Examples include so‐called under‐relaxation coefficients (URCs), which are used to stabilize the evolution of iterative calculation procedures required to solve nonlinear problems. These coefficients are very important since many factors cause virtually all glass‐process simulations to be nonlinear.
URCs have values between 0 and 1, where 1 represents no under‐relaxation and 0 does not allow the estimated field variable to change from one iteration to the next. In general, larger URC values thus allow for more rapid convergence, but divergence will occur instead if a URC is too high. Conversely, small values of URCs tend to be more robust but require many more iterations to satisfy convergence criteria. It remains a bit of an art to specify URCs, especially because optimal values can very much depend on other numerical specifications.
Additional specifications can include the manner in which advection terms are discretized, whether velocity components are solved consecutively as scalar components or coupled to one another, along with pressure, or if energy and radiation equations are solved in a coupled or uncoupled manner. Choosing these options can depend on the capabilities of the computer used as algorithms that couple equations require larger amounts of memory.
As just noted, prescribing numerical parameters is an art so that experience is required for an analyst to become efficient and develop realistic expectations. Nevertheless, many commercial software providers offer recommended or default values to begin a simulation. Most numerical parameters will not affect the converged solution, but only the time required to obtain the solution. However, some numerical schemes will provide more accurate results for a given mesh than others although their differences should become imperceptible with sufficient grid refinement. For example, a second‐order upwind differencing scheme for advection terms will produce less “false diffusion” than a first‐order upwind scheme [7].