page_title: Central differencing scheme
section_title: Conservativeness
hierarchical_section_title: Central differencing scheme / Different aspects of central differencing scheme / Conservativeness
caption_attribution_description: English: it is basically an illustration of consevativeness
context_page_description: 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
context_section_description: Conservation is ensured in central differencing scheme since overall flux balance is obtained by summing the net flux through each control volume taking into account the boundary fluxes for the control volumes around nodes 1 and 4. 
  Boundary flux for control volume around node 1 and 4
  because
caption: Figure 3.Typical illustration
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