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Statements

Subject Item

dbr:Central_differencing_scheme

rdfs:label

Central differencing scheme

rdfs:comment

In applied mathematics, the central differencing scheme is a finite difference method that optimizes the approximation for the differential operator in the central node of the considered patch and provides numerical solutions to differential equations. It is one of the schemes used to solve the integrated convection–diffusion equation and to calculate the transported property Φ at the e and w faces, where e and w are short for east and west (compass directions being customarily used to indicate directions on computational grids). The method's advantages are that it is easy to understand and implement, at least for simple material relations; and that its convergence rate is faster than some other finite differencing methods, such as forward and backward differencing. The right side of the c

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dbr:Control_volume n4:Comparison_.jpg dbr:Bounded_set dbr:Diffusion dbr:Shock_wave dbr:Boundary_layer n4:Typical_Illustration.png dbr:Finite_difference dbr:Upwind_differencing_scheme_for_convection dbr:Péclet_number dbr:Finite_difference_method dbr:Integral dbr:Acceleration n4:Interpolation_value.png dbr:Convection–diffusion_equation dbr:Applied_mathematics dbc:Computational_fluid_dynamics dbr:Taylor_series dbr:List_of_things_named_after_Leonhard_Euler dbc:Finite_differences dbc:Numerical_differential_equations dbr:Convection dbr:Navier–Stokes_equations dbr:Taylor's_theorem dbr:Property dbr:Symmetric_derivative dbr:Continuity_equation dbr:Linear_interpolation dbr:Oscillation dbr:Mass_diffusivity

dbo:abstract

In applied mathematics, the central differencing scheme is a finite difference method that optimizes the approximation for the differential operator in the central node of the considered patch and provides numerical solutions to differential equations. It is one of the schemes used to solve the integrated convection–diffusion equation and to calculate the transported property Φ at the e and w faces, where e and w are short for east and west (compass directions being customarily used to indicate directions on computational grids). The method's advantages are that it is easy to understand and implement, at least for simple material relations; and that its convergence rate is faster than some other finite differencing methods, such as forward and backward differencing. The right side of the convection-diffusion equation, which basically highlights the diffusion terms, can be represented using central difference approximation. To simplify the solution and analysis, linear interpolation can be used logically to compute the cell face values for the left side of this equation, which is nothing but the convective terms. Therefore, cell face values of property for a uniform grid can be written as:

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n17:Central_differencing_scheme