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At least 235 records · Page 13

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The novel implicit and unconditionally stable, high resolution Total Variation Diminishing (TVD) scheme whose application to steady state calculations is presently examined is a member of a one-parameter family of implicit, second-order accurate systems developed by Harten (1983) for the computation of weak solutions for one-dimensional hyperbolic conservation laws. The scheme will not generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments for a quasi-one-dimensional nozzle problem show that the experimentally determined stability limit correlates exactly with the theoretical stability limit for the nonlinear scalar hyberbolic conservation laws.

Yee, H. C.↗

Improving the convergence rate to steady state of parabolic ADI methods

The present, residuals' L(2)-norms analysis of the rate of convergence to steady state for parabolic ADI solvers allows the prediction of the number of iterations required for convergence, as a function of the Courant number alpha. A modification of current ADI codes is presented which significantly improves the convergence rate and is insensitive to the Courant number over a large range of alpha. This corrected algorithm is tested for the cases of Dirichlet problems for uniform grids of many mesh sizes, mixed Dirichlet-Neumann problems, and problems defined on stretched grids and/or problems with variable coefficients.

Abarbanel, Saul S.↗

Steady State Temperature Profile in a Cylinder Heated by Microwaves

A new theory has been developed to calculate the steady state temperature profile in a cylindrical sample positioned along the entire axis of a cylindrical microwave cavity. Temperature profiles where computed for- alumina rods of various radii contained in a cavity excite in one of the TM(sub OnO) modes with n = 1, 2 or 3. Calculations where also performed with a concentric outer cylindrical tube surrounding the rod to investigate hybrid heating. The parameters studies of the sample center and surface temperature where performed as a function of the total power transmitted into the cavity. Also, the total hemispherical emissivity was varied at boundaries of the rod, surrounding tube, and cavity walls. The result are discussed in the context of controlling the average rod temperature and the temperature distribution in the rod during microwave processing.

Jackson, H. W.↗

(abstract) Steady State Temperature Profile in a Cylinder Heated by Microwaves

We have developed a new theory to calculate the steady state temperature profile in a cylindrical sample positioned along the entire axis of a cylindrical microwave cavity. Temperature profiles were computed for alumina rods of various radii excited by one of the TM0n0 modes with n = 1, 2, or 3. Sample surface and center temperatures will be presented as a function of total sample absorbed power or electric field strength at the sample surface. An approach for attaining more uniform heating within the sample by reducing the magnitude of the inverted temperature profile using a concentric outer cylindrical tube will be discussed.

microwave↗

Steady-state temperature distribution in living tissue modeled as cylindrical shells.

Closed form, analytical solutions to the problem of steady-state heat transfer in living tissue modeled as cylindrical shells are presented and discussed. These solutions are particularly useful for the study of temperature distributions in the extremities. Metabolic heat generation, conduction, and heat transported by the blood perfusing the tissue are considered in the model. The results demonstrate the important role that the blood stream plays in the transfer of heat inside living tissue. Solutions are also presented for the limiting cases of diminishing blood flow that would occur during vasoconstriction or occlusion of blood by external means.

Shitzer, A.↗

Nonoscillatory solution of the steady-state inviscid Burgers' equation by mathematical programming

In order to obtain the physically relevant discontinuous numerical solution, the steady-state inviscid Burgers' equation is singularly perturbed through the addition of a small amount of viscosity. A 'cell-centered' finite-difference scheme is proposed which employs two points for the inviscid part and four points for the viscous one. While difficulties are experienced in the capture of interior layers centered at node points, computational results for interior layers centered between node points, and for boundary layers, exhibit accurate nonoscillatory solutions whose discontinuities are captured in one cell on both coarse and fine grids.

Lavery, John E.↗

Steady-state probability density function of the phase error for a DPLL with an integrate-and-dump device

The steady-state behavior of a particular type of digital phase-locked loop (DPLL) with an integrate-and-dump circuit following the phase detector is characterized in terms of the probability density function (pdf) of the phase error in the loop. Although the loop is entirely digital from an implementation standpoint, it operates at two extremely different sampling rates. In particular, the combination of a phase detector and an integrate-and-dump circuit operates at a very high rate whereas the loop update rate is very slow by comparison. Because of this dichotomy, the loop can be analyzed by hybrid analog/digital (s/z domain) techniques. The loop is modeled in such a general fashion that previous analyses of the Real-Time Combiner (RTC), Subcarrier Demodulator Assembly (SDA), and Symbol Synchronization Assembly (SSA) fall out as special cases.

Simon, M.↗