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Petr Fedoseev, Dmitriy Pesterev, Artur Karimov and Denis Butusov
Composition is a powerful and simple approach for obtaining numerical integration methods of high accuracy order while preserving the geometric properties of a basic integrator. Adaptive step size control allows one to significantly increase the performa...
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Zhe Sun, Li-Yuan Dou, Si-Yuan Tan, Zi-Kai Xu, Kamal Djidjeli and Yan Zhou
When dealing with the complex deformation of free surface such as wave breaking, traditional mesh-based Computational Fluid Dynamics (CFD) methods often face problems arising alongside grid distortion and re-meshing. Therefore, the meshless method became...
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Vladimir Lipp, Baerbel Rethfeld, Martin Garcia and Dmitry Ivanov
We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank?Nicolson method with predictor?corrector algorithm and provides h...
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Tobias Martin and Ivan Shevchuk
In this article, the development of high-order semi-implicit interpolation schemes for convection terms on unstructured grids is presented. It is based on weighted essentially non-oscillatory (WENO) reconstructions which can be applied to the evaluation ...
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