Temat: advection-diffusion equation

Skocz do pozycji: 1.

Tytuł:: Two-dimensional model of fluid flow and distribution of nutrient concentration in a microfluidic device
Autorzy:: Wroniszewski, P.
Tematy:: microfluidic device
lab-on-a-chip
advection-diffusion equation
Taylor dispersion; Pokaż więcej
Wydawca:: Politechnika Gdańska
Powiązania:: https://bibliotekanauki.pl/articles/1934016.pdf Link otwiera się w nowym oknie
Opis:: During the past few years, the process of miniaturisation in the field of biochemical laboratory equipment led to the introduction of the so-called "lab-on-a-chip" microdevices, which combine separate functional units into a complex, multifunctional apparatus. Fluid dynamics plays an essential role in the development of such equipment, since frequently the major part of chemical analysis is based on soluble analytes. In this work, we consider a device for the analysis of cell growth under different conditions. In this device, dozens of cell spots absorb the nutrient (analyte) from the liquid medium. The concentration of the analyte must be strictly controlled to maintain a specific microenvironment. A two-dimensional model for the flow field and the distribution of concentration of the analyte is developed taking into account the geometrical shape of the spot with a simplified absorption model. The dependence of the results on the controlling parameters is investigated in order to determine the influence of the presence of the cell spot on the distribution of the analyte.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: The pollutant transport equation for a steady, gradually varied flow in an open channel network: a solution of high accuracy
Autorzy:: Szymkiewicz, R.
Tematy:: steady gradually varied flow
advection-diffusion equation
splitting technique
integral of convolution; Pokaż więcej
Wydawca:: Politechnika Gdańska
Powiązania:: https://bibliotekanauki.pl/articles/1933160.pdf Link otwiera się w nowym oknie
Opis:: The paper is concerned with solving the transport pollutant problem for a steady, gradually varied flow in an open channel network. The 1D advective-diffusive transport equation is solved using the splitting technique. An analytical solution of the linear advective-diffusive equation in the form of an impulse response function is used to solve the advection-diffusion part of the governing equation. This approach, previously applied in solutions of the advection-diffusion equation for a single channel, is extended to a channel network. Numerical calculations are only required to compute the integral of convolution. The finite difference method is used to solve the second part of the governing equation, containing the source term. The applied approach has considerable advantages, especially appreciable in the case of advection-dominated transport with large gradients of concentration, since it generates no numerical dissipation or dispersion. The flow parameters are obtained via solution of the steady, gradually varied flow equation. In the final non-linear system of algebraic equations obtained through approximation of the ordinary differential equation, the depths at each cross-section of channels and the discharge at each branch of the network are considered as unknowns. The system is solved using the modified Picard iteration, which ensures convergence of the iterative process for a steady, gradually varied flow solved for both looped and tree-type open channel networks.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: An accuracy analysis of the cascaded lattice Boltzmann method for the 1D advection-diffusion equation
Autorzy:: Straka, Robert
Sharma, Keerti V.
Tematy:: cascaded thermal lattice Boltzmann method
high order analysis
advection-diffusion equation
equivalent finite difference equation; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/29520238.pdf Link otwiera się w nowym oknie
Opis:: We analyze higher order error terms in a modified partial differential equation of a cascaded lattice Boltzmann method (CLBM) for one conservation law – the advection-diffusion equation. To inspect the behavior of the error terms we derived an equivalent finite difference equation (EFDE), this approach is different from other techniques like the Chapman-Engskog expansion, equivalent partial differential equations or the Maxwell iteration used in the literature. The resulting EFDE is obtained from the recurrence formulas of the lattice Boltzmann equations for the CLBM and is subsequently analyzed by standard analytical techniques. We have found relations of the LBM parameters which could cancel some of the higher order terms, making the method more accurate. The detailed derivation of the EFDE and higher order terms’ pre-factors is the main result of this paper. The resulting explicit form of the error terms are derived and presented.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: The Dirichlet problem for the time-fractional advection-diffusion equation in a half-space
Autorzy:: Povstenko, Y.
Klekot, J.
Tematy:: Caputo fractional derivative
advection-diffusion equation
Laplace integral transform
Fourier sine transform
Mittag-Leffler function
pochodna rzędu ułamkowego Caputo
funkcja Mittag-Lefflera; Pokaż więcej
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Powiązania:: https://bibliotekanauki.pl/articles/122941.pdf Link otwiera się w nowym oknie
Opis:: The one-dimensional time-fractional advection-diffusion equation with the Caputo time derivative is considered in a half-space. The fundamental solution to the Dirichlet problem and the solution of the problem with constant boundary condition are obtained using the integral transform technique. The numerical results are illustrated graphically.
Dostawca treści:: Biblioteka Nauki

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