An Arbitrary-Lagrangian-Eulerian High-Order Gas-Kinetic Scheme for Three-Dimensional Computations

The aim of this paper is to present an application of high-order numerical analysis methods to a simulation system that models the movement of a cylindrical-shaped object (mine, projectile, etc.) in a marine environment and in general in fluids with important applications in Naval operations. More specifically, an alternative methodology is proposed for the dynamics of the Navy’s three-dimensional mine impact burial prediction model, Impact35/vortex, based on the Dormand–Prince Runge–Kutta fifth-order and the singly diagonally implicit Runge–Kutta fifth-order methods. The main aim is to improve the time efficiency of the system, while keeping the deviation levels of the final results, derived from the standard and the proposed methodology, low.

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High-order compact LOD methods for solving high-dimensional advection equations

Computational and Applied Mathematics ◽

10.1007/s40314-021-01483-w ◽

2021 ◽

Vol 40 (3) ◽

Author(s):

Bo Hou ◽

Yongbin Ge

Keyword(s):

Truncation Error ◽

Three Dimensional ◽

Taylor Series Expansion ◽

High Order ◽

High Dimensional ◽

Analysis Method ◽

Order Accuracy ◽

Von Neumann ◽

One Dimensional ◽

Von Neumann Analysis

AbstractIn this paper, by using the local one-dimensional (LOD) method, Taylor series expansion and correction for the third derivatives in the truncation error remainder, two high-order compact LOD schemes are established for solving the two- and three- dimensional advection equations, respectively. They have the fourth-order accuracy in both time and space. By the von Neumann analysis method, it shows that the two schemes are unconditionally stable. Besides, the consistency and convergence of them are also proved. Finally, numerical experiments are given to confirm the accuracy and efficiency of the present schemes.

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Three-dimensional vectorial analysis of an electromagnetic non-diffracting high-order Bessel trigonometric beam

Wave Motion ◽

10.1016/j.wavemoti.2012.03.002 ◽

2012 ◽

Vol 49 (5) ◽

pp. 561-568 ◽

Cited By ~ 9

Author(s):

F.G. Mitri

Keyword(s):

Three Dimensional ◽

High Order

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VERY HIGH-ORDER SPATIALLY IMPLICIT SCHEMES FOR COMPUTATIONAL ACOUSTICS ON CURVILINEAR MESHES

Journal of Computational Acoustics ◽

10.1142/s0218396x01000541 ◽

2001 ◽

Vol 09 (04) ◽

pp. 1259-1286 ◽

Cited By ~ 254

Author(s):

MIGUEL R. VISBAL ◽

DATTA V. GAITONDE

Keyword(s):

Three Dimensional ◽

Radiation Condition ◽

Higher Order ◽

High Order ◽

High Frequencies ◽

Decomposition Strategies ◽

The Impact ◽

Spurious Modes ◽

Very High ◽

Computational Strategy

A high-order compact-differencing and filtering algorithm, coupled with the classical fourth-order Runge–Kutta scheme, is developed and implemented to simulate aeroacoustic phenomena on curvilinear geometries. Several issues pertinent to the use of such schemes are addressed. The impact of mesh stretching in the generation of high-frequency spurious modes is examined and the need for a discriminating higher-order filter procedure is established and resolved. The incorporation of these filtering techniques also permits a robust treatment of outflow radiation condition by taking advantage of energy transfer to high-frequencies caused by rapid mesh stretching. For conditions on the scatterer, higher-order one-sided filter treatments are shown to be superior in terms of accuracy and stability compared to standard explicit variations. Computations demonstrate that these algorithmic components are also crucial to the success of interface treatments created in multi-domain and domain-decomposition strategies. For three-dimensional computations, special metric relations are employed to assure the fidelity of the scheme in highly curvilinear meshes. A variety of problems, including several benchmark computations, demonstrate the success of the overall computational strategy.

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