Central differencing scheme

In applied mathematics, the central differencing scheme is a finite difference method. The finite difference method optimizes the approximation for the differential operator in the central node of the considered patch and provides numerical solutions to differential equations. The central differencing scheme 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. The advantages of this method are that it is easy to understand and to 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 hand side of the convection-diffusion equation which basically highlights the diffusion terms can be represented using central difference approximation. Thus, in order to simplify the solution and analysis, linear interpolation can be used logically to compute the cell face values for the left hand 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 In applied mathematics, the central differencing scheme is a finite difference method. The finite difference method optimizes the approximation for the differential operator in the central node of the considered patch and provides numerical solutions to differential equations. The central differencing scheme 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. The advantages of this method are that it is easy to understand and to 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 hand side of the convection-diffusion equation which basically highlights the diffusion terms can be represented using central difference approximation. Thus, in order to simplify the solution and analysis, linear interpolation can be used logically to compute the cell face values for the left hand 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 The convection–diffusion equation is a collective representation of both diffusion and convection equations and describes or explains every physical phenomenon involving the two processes: convection and diffusion in transferring of particles, energy or other physical quantities inside a physical system. The convection-diffusion is as follows: here Г is diffusion coefficient and Φ is the property Formal integration of steady-state convection–diffusion equation over a control volume gives