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High order precision estimates are obtained for the proposed algorithm.
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So this study utilizes WENO procedures to achieve a uniform high-order precision.
The scheme obtained high-order precision with Cartesian and cylindrical coordinates.
The method can keep the scheme with negative weights steady and achieve high-order precision.
In this sense, high-order precision is gained though less computational stencils are used.
As everyone knows, the WENO schemes can achieve high-order precision and capture shock at the discontinuities.
The designed method, without restriction about the CFL time step, maintains uniform high-order precision in both space and time.
The semi-Lagrangian scheme maintains uniform high-order precision and non-oscillatory shock transitions near discontinuities, which simultaneously allowed weaker CFL conditions to ensure computational efficiency.
end{aligned} (1.1) For problems such as these, this paper develops a series of semi-Lagrangian finite volume (SL-FV) WENO schemes which allow for weaker CFL conditions, while maintaining high-order precision and preventing shock transitions near discontinuities.
To handle this problem, we replace (c_{tau}) in (2.3) with nonlinear weights (omega_{tau}), which result in an approach is high-order precision and non-oscillatory at the discontinuities.
Spheres of radii (non-dimensionalized in terms of a mean free path) in the range 10−6 106 are considered, and a transformation of the range from (R, ∞) to (0, 1), is used together with successively high order quadratures, and high precision in all computations.
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