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Compared to other existing methods, our method is more accurate and simpler to implement, and moreover it closely resembles the central difference scheme for the classical Laplace operator.
In the chosen method the equations of motion are solved by the central difference scheme.
It, indeed, comes from the truncation error of the central difference scheme used by them.
Unlike the central difference scheme, the upwind difference scheme was found not to require a kinetic energy conservation property to control aliasing error.
The angular and spatial discretizations of the discrete-ordinates equation were achieved using the T3 quadrature set and the central difference scheme, respectively.
The resolution is easily performed with a step-by-step solution technique using the central difference scheme to solve the coupled equation system.
The convective terms were discretized using second-order upwind scheme, and the pressure was interpolated using linear interpolation scheme, while the central difference scheme was utilized for diffusion terms.
We apply the central difference methods to the spatial operators and obtain that the numerical schemes are convergent with orders (O tau^{q} + h^{2})) ((q = 1,2,3,4,5)).
These schemes are used with a 5th-order WENO scheme for inviscid flux and the stencil width of the central differencing scheme is designed to be within that of the WENO scheme.
The central differencing schemes achieve the maximum order of accuracy in the stencil.
By employing the standard high-order finite difference schemes to discretize the Laplacian, the present MIB method automatically reduces to the standard central difference scheme when the interface is absent.
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