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Founded in 1876, Texas A&M University is a U.S. public and comprehensive university offering a wide variety of academic programs far beyond its original label of agricultural and mechanical trainings. It is one of the few institutions holding triple federal designations as a land-, sea- and ...
In numerical modeling, a numerical computational scheme is said to be consistent if the discrete algebraic equations created by the process of discretization recover or reduce to the original continuum differential equations as the spacing in the computational grid is shrunk to zero. The scheme is said to be unconditionally consistent if the above is true no matter how (i.e. in what order, etc.) the grid is shrunk. Thus consistency deals with relations between equations in their continuum versus discrete forms, as opposed to convergence.
Industry:Earth science
In numerical modeling, a numerical computational scheme is said to be convergent is the solutions to the discrete algebraic equations created by the process of discretization approach the solutions of the original continuum differential equations as the spacing in the computational grid is shrunk to zero. Thus convergence deals with relations between solutions of equations in their continuum versus discrete forms, as opposed to consistency.
Industry:Earth science
In numerical modeling, a numerical computational scheme is said to be stable if the infinite set of computed solutions of the discrete algebraic equations created by the process of discretization of some original continuum differential equations is always below some uniformly bounded upper-limit as the computational grid spacing is shrunk to zero. There are reasonably efficacious methods for exploring the stabilility of a given linear set of discretized equations, although it is much trickier with nonlinear equations, with the most popular option for the latter being the linearization thereof.
Industry:Earth science
In numerical modeling, a system of vertical coordinates where an arbitrary number of layers are specified in which some fluid property (e.g. density) remains constant, i.e. an independent variable. The dependent variable is the vertical extent of each layer. Pressure coordinates are an example of layer coordinates. Compare to level coordinates.
Industry:Earth science
In numerical modeling, a vertical coordinate system in which a arbitrary number of height or depth levels are specified at which the changing values of the various dependent variables are calculated. Thus the level heights or depths are independent variables. Compare to layer coordinates.
Industry:Earth science
In numerical modeling, an approximation which uses interpolating functions to estimate derivatives of fields represented on a grid in physical space. It is so-called because the interpolating functions used are usually the same as are used in the spectral method. All operations other than differentiation are carried out in the physical space defined by the grid rather than in spectral space. This allows, for example, the calculation of the nonlinear terms, a dauntingly onerous task in spectral space, to be easily performed. The trade-off is that the calculations are aliased, although various remedies for the problem have been proposed.
Industry:Earth science
In numerical modeling, an equation is diagnostic if the present value of a dependent variable is calculated from the present value(s) of one or more dependent variables.
Industry:Earth science
In numerical modeling, an equation is prognostic if the future value of a dependent variable is predicted from the present value(s) of one or more dependent variables.
Industry:Earth science
In numerical modeling, an integration algorithmthat temporally advances an approximate solution via discrete steps using information from present as well as from previous time steps. These are computationally more complex than explicit schemes but allow longer time stepping intervals and usually have better numerical stability properties.
Industry:Earth science
In numerical modeling, the distance between contiguous points in the computational grid. This can refer to either temporal or spatial resolution, with the two being dependent in procedures using both.
Industry:Earth science
