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Search results for: diffusive wave equation
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Verification of algorithms determining wave loads on support structure of wind turbine
PublicationThe 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
PublicationThe 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...
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Existence and uniqueness of monotone and bounded solutions for a finite-difference discretization a` la Mickens of the generalized Burgers–Huxley equation.
PublicationDeparting from a generalized Burgers–Huxley partial differential equation, we provide a Mickens-type, nonlinear, finite-difference discretization of this model. The continuous system is a nonlinear regime for which the existence of travelling-wave solutions has been established previously in the literature. We prove that the method proposed also preserves many of the relevant characteristics of these solutions, such as the positivity,...
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The finite-difference simulation of x-rays propagation through a system of lenses
PublicationThe propagation of X-ray waves through an optical system consisting of 33 aluminum X-ray refractive lenses is considered. For solving the problem, a finite-difference method is suggested and investigated. It is shown that very small steps of the difference grid are necessary for reliable computation of propagation of X-ray waves through the system of lenses. It is shown that the wave phase is a function very quickly increasing...
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About definition of modes and magnetosonic heating in a plasma’s flow: Especial cases of perpendicular and nearly perpendicular wave vector and magnetic field
PublicationDynamics of hydrodynamic perturbations in a plasma depend strongly on an angle between the wave vector and equilibrium straight magnetic field. The case of perpendicular propagation is especial. There are only two (fast) magnetosonic modes since two (slow) ones degenerate into the stationary one with zero speed of propagation. This demands individual definition of wave modes by the links of hydrodynamic relations. These links are...
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Flood Routing by the Non-Linear Muskingum Model: Conservation of Mass and Momentum
PublicationIn this paper, the conservative properties of the Muskingum equation, commonly applied to solve river flood routing, are analysed. The aim of this analysis is to explain the causes ofthe mass balance error, which is observed in the numerical solutions of its non-linear form. The linear Muskingum model has been considered as a semi-discrete form of the kinematic wave equation and therefore it was possible to derive its two non-linear...
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ADAPTIVE METHOD FOR THE SOLUTION OF 1D AND 2D ADVECTION-DIFFUSION EQUATIONS USED IN ENVIRONMENTAL ENGINEERING
PublicationThe paper concerns the numerical solution of one-dimensional (1D) and two-dimensional (2D) advection-diffusion equations. For the numerical solution of the 1D advection-diffusion equation a method, originally proposed for solution of the 1D pure advection equation, has been developed. A modified equation analysis carried out for the proposed method allowed increasing of the resulting solution accuracy and consequently, to reduce...
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Coherent-wave Monte Carlo method for simulating light propagation in tissue
PublicationSimulating propagation and scattering of coherent light in turbid media, such as biological tissues, is a complex problem. Numerical methods for solving Helmholtz or wave equation (e.g. finite-difference or finite-element methods) require large amount of computer memory and long computation time. This makes them impractical for simulating laser beam propagation into deep layers of tissue. Other group of methods, based on radiative...
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A high-accuracy complex-phase method of simulating X-ray propagation through a multi-lens system
PublicationThe propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. For solving the problem for an electromagnetic wave, a finite-difference method is applied. The error of simulation is analytically estimated and investigated. It was found that a very detailed difference grid is required for reliable and accurate calculations of the propagation of X-ray waves through a multi-lens...
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The finite difference methods of computation of X-rays propagation through a system of many lenses
PublicationThe propagation of X-ray waves through an optical system consisting of many beryllium X-ray refrac- tive lenses is considered. In order to calculate the propagation of electromagnetic in the optical sys- tem, two differential equations are considered. First equation for an electric field of a monochromatic wave and the second equation derived for complex phase of the same electric The propagation of X-ray waves through an optical system...
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On the convergence of a nonlinear finite-difference discretization of the generalized Burgers–Fisher equation
PublicationIn this note, we establish analytically the convergence of a nonlinear finite-difference discretization of the generalized Burgers-Fisher equation. The existence and uniqueness of positive, bounded and monotone solutions for this scheme was recently established in [J. Diff. Eq. Appl. 19, 1907{1920 (2014)]. In the present work, we prove additionally that the method is convergent of order one in time, and of order two in space. Some...
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A high-accuracy method of computation of x-ray waves propagation through an optical system consisting of many lenses
PublicationThe propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. Two differential equations are contemplated for solving the problem for electromagnetic wave propagation: first – an equation for the electric field, second – an equation derived for a complex phase of an electric field. Both equations are solved by the use of a finite-difference method. The simulation error is estimated...
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Balance errors generated by numerical diffusion in the solution of non-linear open channel flow equations
PublicationThe paper concerns the untypical aspect of application of the dissipative numerical methods to solve nonlinear hyperbolic partial differential equations used in open channel hydraulics. It is shown that in some cases the numerical diffusion generated by the applied method of solution produces not only inaccurate solution but as well as a balance error. This error may occur even for an equation written in the conservative form not...
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Importance of sign conventions on analytical solutions to the wave-induced cyclic response of a poro-elastic seabed
PublicationThis paper discusses the influence of different sign conventions for strains and stresses, i.e. the solid mechanics sign convention and the soil mechanics sign convention, on the form of governing partial differential equations (the static equilibrium equations and the continuity equation) used to describe the wave-induced cyclic response of a poro-elastic seabed due to propagation of a sinusoidal surface water-wave. Some selected...
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An Experimental Investigation of Pressure Wave Celerity During the Transient Slurry Flow
PublicationTransportation of slurries in pressure pipelines is an example of a complex flow due to specific parameters of transported medium. For practitioners, the economy of designing and maintenance is usually the most important factor. For this reason, most of hydrotransport installations are fairly simple; however, they become more vulnerable to negative effects of the transient flow which can occur in pressure pipelines. As the consequence,...
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Nonlinear Interaction of Magnetoacoustic Modes in a Quasi-Isentropic Plasma Flow
PublicationThe nonlinear interaction of magnetoacoustic waves in a plasma is analytically studied. A plasma is an open system. It is affected by the straight constant equilibrium magnetic flux density forming constant angle with the wave vector which varies from 0 till . The nonlinear instantaneous equation which describes excitation of secondary wave modes in the field of intense magnetoacoustic perturbations is derived by use of projecting....
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Absorbing Boundary Conditions Derived Based on Pauli Matrices Algebra
PublicationIn this letter, we demonstrate that a set of absorbing boundary conditions (ABCs) for numerical simulations of waves, proposed originally by Engquist and Majda and later generalized by Trefethen and Halpern, can alternatively be derived with the use of Pauli matrices algebra. Hence a novel approach to the derivation of one-way wave equations in electromagnetics is proposed. That is, the classical wave equation can be factorized...
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TIME-AND-SPACE STRUCTURE OF FORCE-DRIVEN RIGID SPHEREWAVEFIELD
PublicationThis paper introduces a time-domain, causality-inspired description of a vector-source acoustic wavefield of arbitrary time evolution, where a sphere is a practical realisation of quasi-point contact surface without which a point force would not be able to exert an impact onto non-viscous fluid. At every space location, the resulting acoustic field is described by a pair of physical variables characterising the time evolution of...
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Marek Czachor prof. dr hab.
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Magnetosonic Excitation of the Entropy Perturbations in a Plasma with Thermal Conduction Depending on Temperature
PublicationNonlinear excitation of the entropy perturbations by magnetosonic waves in a uniform and infinite plasma model is considered. The wave vector of slow or fast mode forms an arbitrary angle (0 B B ) with the equilibrium straight magnetic field, and all perturbations are functions of the time and longitudinal coordinate. Thermal conduction is the only factor which destroys isentropicity of wave perturbations and causes the nonlinear...