Topic
Finite difference method
About: Finite difference method is a research topic. Over the lifetime, 21603 publications have been published within this topic receiving 468852 citations. The topic is also known as: Finite-difference methods & FDM.
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TL;DR: In this article, a numerical study of the three-dimensional fluid dynamics inside a model left ventricle during diastole is presented, which is modelled as a portion of a prolate spheroid with a moving wall, whose dynamics is externally forced to agree with a simplified waveform of the entering flow.
Abstract: A numerical study of the three-dimensional fluid dynamics inside a model left ventricle during diastole is presented. The ventricle is modelled as a portion of a prolate spheroid with a moving wall, whose dynamics is externally forced to agree with a simplified waveform of the entering flow. The flow equations are written in the meridian body-fitted system of coordinates, and expanded in the azimuthal direction using the Fourier representation. The harmonics of the dependent variables are normalized in such a way that they automatically satisfy the high-order regularity conditions of the solution at the singular axis of the system of coordinates. The resulting equations are solved numerically using a mixed spectral–finite differences technique. The flow dynamics is analysed by varying the governing parameters, in order to understand the main fluid phenomena in an expanding ventricle, and to obtain some insight into the physiological pattern commonly detected. The flow is characterized by a well-defined structure of vorticity that is found to be the same for all values of the parameters, until, at low values of the Strouhal number, the flow develops weak turbulence.
147 citations
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TL;DR: In this article, the authors propose a new procedure for designing by rote finite difference schemes that inherit energy conservation or dissipation property from nonlinear partial differential equations, such as the Korteweg-de Vries (KdV) equation and the Cahn-Hilliard equation.
147 citations
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TL;DR: In this paper, the authors derived the necessary extension to the FDTD equations to accommodate nondiagonal tensors and obtained excellent agreement between FDTD and exact analytic results for a one-dimensional anisotropic scatterer.
Abstract: The popularity of the finite-difference time-domain (FDTD) method stems from the fact that it is not limited to a specific geometry and it does not restrict the constitutive parameters of a scatterer. Furthermore, it provides a direct solution to problems with transient illumination, but can also be used for harmonic analysis. However, researchers have limited their investigation to materials that are either isotropic or that have diagonal permittivity, conductivity, and permeability tensors. The authors derive the necessary extension to the FDTD equations to accommodate nondiagonal tensors. Excellent agreement between FDTD and exact analytic results is obtained for a one-dimensional anisotropic scatterer. >
147 citations
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TL;DR: Numerical tests revealed that if the number of points selected by DEIM algorithm reached 50, the approximation errors due to POD/DEIM and POD reduced systems have the same orders of magnitude, thus supporting the theoretical results existing in the literature.
147 citations
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TL;DR: In this paper, a high-order accurate method for solving the one-dimensional heat and advection-diffusion equations is proposed, which has fourth-order accuracy in both space and time variables, i.e. this method is of order O( h 4, k 4 ).
147 citations