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Full-Text Articles in Engineering
A Hybrid Finite Difference Method For Singularly Perturbed Delay Partial Differential Equations With Discontinuous Coefficient And Source, Nitika Sharma, Aditya Kaushik
A Hybrid Finite Difference Method For Singularly Perturbed Delay Partial Differential Equations With Discontinuous Coefficient And Source, Nitika Sharma, Aditya Kaushik
Journal of Marine Science and Technology
The article presents a hybrid finite difference scheme to solve a singularly perturbed parabolic functional differential equation with discontinuous coefficient and source. The simultaneous presence of deviating argument with a discontinuous source and coefficient makes the problem stiff. The solution of the problem exhibits turning point behaviour across discontinuity as tends to zero. The hybrid scheme presented is a composition of a central difference scheme and a midpoint upwind scheme on a specially generated mesh. At the same time, an implicit finite difference method is used to discretize the time variable. Consistency, stability, and convergence of the presented numerical approach …
Transient Response Of Sloshing Fluid In A Three Dimensional Tank, Chih-Hua Wu, Bang-Fuh Chen
Transient Response Of Sloshing Fluid In A Three Dimensional Tank, Chih-Hua Wu, Bang-Fuh Chen
Journal of Marine Science and Technology
Sloshing waves in moving tanks have been studied numerically, theoretically and experimentally in the past several decades. Most reported studies have been for tanks excited by forcing motion in a limited number of directions and with fixed excitation frequencies throughout the forcing. In the present study, a time-independent finite difference method is used to simulate fluid sloshing in the three-dimensional tanks with arbitrary depths and the tanks are subject to a range of excitation frequencies with motions that exhibit multiple degrees of freedom. The developed numerical scheme is verified by rigorous benchmark tests, and the advantage and efficiency of the …