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Wyniki wyszukiwania dla: PARAXIAL WAVE EQUATION
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Modelling of FloodWave Propagation with Wet-dry Front by One-dimensional Diffusive Wave Equation
PublikacjaA full dynamic model in the form of the shallow water equations (SWE) is often useful for reproducing the unsteady flow in open channels, as well as over a floodplain. However, most of the numerical algorithms applied to the solution of the SWE fail when flood wave propagation over an initially dry area is simulated. The main problems are related to the very small or negative values of water depths occurring in the vicinity of...
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Computationally Effcient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems
PublikacjaThis paper presents a study dealing with increasing the computational efficiency in modeling floodplain inundation using a two-dimensional diffusive wave equation. To this end, the domain decomposition technique was used. The resulting one-dimensional diffusion equations were approximated in space with the modified finite element scheme, whereas time integration was carried out using the implicit two-level scheme. The proposed...
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Analysis of Floodplain Inundation Using 2D Nonlinear Diffusive Wave Equation Solved with Splitting Technique
PublikacjaIn the paper a solution of two-dimensional (2D) nonlinear diffusive wave equation in a partially dry and wet domain is considered. The splitting technique which allows to reduce 2D problem into the sequence of one-dimensional (1D) problems is applied. The obtained 1D equations with regard to x and y are spatially discretized using the modified finite element method with the linear shape functions. The applied modification referring...
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Impact of the Finite Element Mesh Structure on the Solution Accuracy of a Two-Dimensional Kinematic Wave Equation
PublikacjaThe paper presents the influence of the finite element mesh structure on the accuracy of the numerical solution of a two-dimensional linear kinematic wave equation. This equation was solved using a two-level scheme for time integration and a modified finite element method with triangular elements for space discretization. The accuracy analysis of the applied scheme was performed using a modified equation method for three different...
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Simulation of unsteady flow over floodplain using the diffusive wave equation and the modified finite element method
PublikacjaWe consider solution of 2D nonlinear diffusive wave equation in a domain temporarily covered by a layer of water. A modified finite element method with triangular elements and linear shape functions is used for spatial discretization. The proposed modification refers to the procedure of spatial integration and leads to a more general algorithm involving a weighting parameter. The standard finite element method and the finite difference...
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Impact of diffusion coefficient averaging on solution accuracy of the 2D nonlinear diffusive wave equation for floodplain inundation
PublikacjaIn the study, the averaging technique of diffusion coefficients in the two-dimensional nonlinear diffusive wave equation applied to the floodplain inundation is presented. As a method of solution, the splitting technique and the modified finite element method with linear shape functions are used. On the stage of spatial integration, it is often assumed that diffusion coefficient is constant over element and equal to its average...
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Discussion of “Development of an Accurate Time integration Technique for the Assessment of Q-Based versus h-Based Formulations of the Diffusion Wave Equation for Flow Routing” by K. Hasanvand, M.R. Hashemi and M.J. Abedini
PublikacjaThe discusser read the original with great interest. It seems, however, that some aspects of the original paper need additional comments. The authors of the original paper discuss the accuracy of a numerical solution of the diffusion wave equation formulated with respect to different state variables. The analysis focuses on nonlinear equations in the form of a single transport equation with the discharge Q (volumetric flow rate)...
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Efficient quadrature for fast oscillating integralof paraxial optics
PublikacjaThe study concerns the determination of quadrature for the integral solutionof the paraxial wave equation. The difficulty in computation of the integral isassociated with the rapid change of the integrand phase. The developed quadraturetakes into account the fast oscillating character of the integrand. The presentedmethod is an alternative to the commonly used methods based on the use of theFourier transform. The determination...
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Data obtained by computation for X-ray focusing using oriented Gaussian beams
Dane BadawczeThe propagation of X-ray waves through an optical system consisting of several X-ray refractive lenses is considered. Gaussian beams are exact solutions of the paraxial equation. The Helmholtz equation describes the propagation of a monochromatic electromagnetic wave. Since the widths of the beams are much larger than the wavelength of X-rays, Gaussian...
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Database of the illustrative simulations of the nonstandard approximation of the generalized Burgers–Huxley equation
Dane BadawczeThe presented dataset is a result of numerical analysis of a generalized Burgers–Huxley partial differential equation. An analyzed diffusive partial differential equation consist with nonlinear advection and reaction. The reaction term is a generalized form of the reaction law of the Hodgkin–Huxley model, while the advection is a generalized form of...
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0,1].
Dane BadawczeThe presented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation.
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Potential energy curve, rovibrational energies and nuclear wave functions of 2 singlet Pi state in KLi dimer
Dane BadawczeThis data sets contains potential energy curve, energy levels and nuclear wave functions of rovibrational states of KLi dimer in 2 singlet Pi electronic state. Potential energy curve (PEC) for the electronic state was calculated in the Born-Oppenheimer approximation by the means of effective core potentials and MRCI method. Nuclear wave functions and...
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Database of the convergence analysis results of the nonstandard approximation of the generalized Burgers–Huxley equation for the solution bounded within [0, γ^(1/p)].
Dane BadawczePresented dataset is a result of the convergence analysis of the Mickens-type, nonlinear, finite-difference discretization of a generalized Burgers–Huxley partial differential equation. The generalized Burgers–Huxley equation is a diffusive partial differential equation with nonlinear advection and diffusion. The boundary problem for this equation possesses...
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Dimensionally Consistent Nonlinear Muskingum Equation
PublikacjaAlthough the Muskingum equation was proposed nearly 75 years ago, it is still a subject of active research. Despite of its simple form, the real properties of this equation have not been comprehensively explained. This paper proposes a new interpretation of the linear McCarthy’s relation. This relation can be interpreted only together with the storage equation, whereas the Muskingum equation can be derived directly from the system...
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Identification of Parameters Influencing the Accuracy of the Solution of the Nonlinear Muskingum Equation
PublikacjaTwo nonlinear versions of the Muskingum equation are considered. The difference between both equations relates to the exponent parameter. In the first version, commonly used in hydrology, this parameter is considered as free, while in the second version, it takes a value resulting from the kinematic wave theory. Consequently, the first version of the equation is dimensionally inconsistent, whereas the proposed second one is consistent. It...
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Some new soliton solutions to the higher dimensional Burger–Huxley and Shallow water waves equation with couple of integration architectonic
PublikacjaIn this paper, we retrieve some traveling wave, periodic solutions, bell shaped, rational, kink and anti-kink type and Jacobi elliptic functions of Burger’s equation and Shallow water wave equation with the aid of various integration schemes like improved -expansion scheme and Jacobi elliptic function method respectively. We also present our solutions graphically in various dimensions.
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Waves Along Fractal Coastlines: From Fractal Arithmetic to Wave Equations
PublikacjaBeginning with addition and multiplication intrinsic to a Koch-type curve, we formulate and solve wave equation describing wave propagation along a fractal coastline. As opposed to examples known from the literature, we do not replace the fractal by the continuum in which it is embedded. This seems to be the first example of a truly intrinsic description of wave propagation along a fractal curve. The theory is relativistically...
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Inverse Flood Routing Using Simplified Flow Equations
PublikacjaThe paper considers the problem of inverse flood routing in reservoir operation strategy. The aim of the work is to investigate the possibility of determining the hydrograph at the upstream end based on the hydrograph required at the downstream end using simplified open channel flow models. To accomplish this, the linear kinematic wave equation, the diffusive wave equation and the linear Muskingum equation are considered. To achieve...
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Verification of algorithms determining wave loads on support structure of wind turbine
PublikacjaThe offshore wind turbines require determination of wave loads on their support structure. This structure is fixed and, therefore, this problem is reduced to solving only the diffraction problem, which is determined by Laplace equation and conditions on the following boundaries: on the support structure, on the sea free surface and on its bottom, and at infinity on free surface. The linear problem was applied to determine the wave...
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Studies of Nonlinear Sound Dynamics in Fluids Based on the Caloric Equation of State
PublikacjaThe sound speed and parameters of nonlinearity B/A, C/A in a fluid are expressed in terms of coefficients in the Taylor series expansion of an excess internal energy, in powers of excess pressure and density. That allows to conclude about features of the sound propagation in fluids, the internal energy of which is known as a function of pressure and density. The sound speed and parameters of nonlinearity in the mixture consisting...