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The objective of this paper is to investigate how well numerical steady-state solutions can mimic true steady-states of a model nonlinear reaction-convection. In order to assess the possible'sourcesoferrors,slowconvergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach, six different numerical aspects are addressed. First, spurious stable and unstable steady-state numerical solutions (numerically irrelevant solutions) can be independently introduced by spatial and temporal discretizations satisfying the same boundary condition and initial data. Second, the various numerical treatments of the reaction term can affect the stability of the spurious as well as the exact steady-state solutions. Third, the time discretization can destabilize the spurious stable steady-state numerical solutions that are introduced by the spatial discretizations or vice versa. Fourth, for a given finite difference method, the strength of the coefficient of the convection ter...

The body normally hosts a variety of saprotrophic micro-organisms that may cause infection. Athlete's foot causes scaling, flaking and itching of the affected skin. Blisters and cracked skin may also occur, leading to exposed raw tissue, pain, swelling and inflammation. Secondary bacterial infection can accompany the fungal infection. This work examined the anti-fungal activity of Ardisia crispa (AC) against common fungi that cause Athlete’s foot and several other pathogenic fungi. The antimicrobial activity of water, ethanol and chloroform extracts of AC was tested against fungal strains using the disc diffusion method. This antimicrobial activity was compared to standard antifungal drugs (griseofulvin, fluconazole and itraconazole). Results revealed that chloroform extract of AC had potent anti-fungal activity against Trichophyton rubrum ATCC 40051 andTrichophyton mentagrophytes ATCC 40004 which are the two most commonly cause of Athlete’s foot. Moderate activity was observed against Candida albicans ATCC 14053,Candida tropicalis ATCC 14056, Microsporum canis (clinical isolates and identified at the Department of Pathology and Microbiology, Universiti Putra Malaysia) and Aspergillus fumigatus ATCC 14109. The ethanol extract only had mild activity against the Candidia spp and the water extract was devoid of any activity. The anti-fungal activity of chloroform extract was statistically more potent than griseofulvin but less potent than fluconazole and itraconazole. Findings from current study support the use of AC in traditional medicine for the treatment of various fungal infections and may potentially be used in the treatment of athlete’s foot. Key words: Ardisia crispa, anti-fungal, athlete’s foot.

A complex two-dimensional, unsteady, viscous hypersonic shock wave interaction is numerically simulated by a high-resolution, second-order fully implicit shock-capturing scheme. The physical model consists of a non-stationary oblique shock impinging on the bow shock of a blunt body. Studies indicate that the unsteady flow patterns are slightly different from their steady counterparts. However, for the sample cases investigated the peak surface pressures for the unsteady flows seem to occur at very different impingement locations than for the steady flow cases.

The goal is to extend our adaptive numerical dissipation control in high order filter schemes and our new divergence-free methods for ideal MHD to non-ideal MHD that include viscosity and resistivity. The key idea consists of automatic detection of different flow features as distinct sensors to signal the appropriate type and amount of numerical dissipation/filter where needed and leave the rest of the region free of numerical dissipation contamination. These scheme-independent detectors are capable of distinguishing shocks/shears, flame sheets, turbulent fluctuations and spurious high-frequency oscillations. The detection algorithm is based on an artificial compression method (ACM) (for shocks/shears), and redundant multi-resolution wavelets (WAV) (for the above types of flow feature). These filter approaches also provide a natural and efficient way for the minimization of Div(B) numerical error. The filter scheme consists of spatially sixth order or higher non-dissipative spatial difference operators as the base scheme for the inviscid flux derivatives. If necessary, a small amount of high order linear dissipation is used to remove spurious high frequency oscillations. For example, an eighth-order centered linear dissipation (AD8) might be included in conjunction with a spatially sixth-order base scheme. The inviscid difference operator is applied twice for the viscous flux derivatives. After the completion of a full time step of the base scheme step, the solution is adaptively filtered by the product of a 'flow detector' and the 'nonlinear dissipative portion' of a high-resolution shock-capturing scheme. In addition, the scheme independent wavelet flow detector can be used in conjunction with spatially compact, spectral or spectral element type of base schemes. The ACM and wavelet filter schemes using the dissipative portion of a second-order shock-capturing scheme with sixth-order spatial central base scheme for both the inviscid and viscous MHD flux derivatives and a fourth-order Runge-Kutta method are denoted.

Characteristic-based explicit and implicit total variation diminishing (TVD) schemes for the two-dimensional compressible Euler equations have recently been developed. This is a generalization of recent work of Roe and Davis to a wider class of symmetric (non-upwind) TVD schemes other than Lax-Wendroff. The Roe and Davis schemes can be viewed as a subset of the class of explicit methods. The main properties of the present class of schemes are that they can be implicit, and, when steady-state calculations are sought, the numerical solution is independent of the time step. In a recent paper, a comparison of a linearized form of the present implicit symmetric TVD scheme with an implicit upwind TVD scheme originally developed by Harten and modified by Yee was given. Results favored the symmetric method. It was found that the latter is just as accurate as the upwind method while requiring less computational effort. Currently, more numerical experiments are being conducted on time-accurate calculations and on the effect of grid topology, numerical boundary condition procedures, and different flow conditions on the behavior of the method for steady-state applications. The purpose here is to report experiences with this type of scheme and give guidelines for its use.

The casing of large electrical generators can be deformed slightly by the rotor''s magnetic field. The sound emission produced by these periodic deformations, which could possibly exceed guaranteed noise emission limits, is analyzed analytically and numerically. From the deformation of the casing, the normal velocity of the generator''s surface is computed. Taking into account the corresponding symmetry, an analytical solution for the acoustic pressure outside the generator is found in terms of the Hankel function of second order. The normal velocity of the generator surface provides the required boundary condition for the acoustic pressure and determines the magnitude of pressure oscillations. For the numerical simulation, the nonlinear 2D Euler equations are formulated in a perturbation form for low Mach number Computational Aeroacoustics (CAA). The spatial derivatives are discretized by the classical sixth-order central interior scheme and a third-order boundary scheme. Spurious high frequency oscillations are damped by a characteristic-based artificial compression method (ACM) filter. The time derivatives are approximated by the classical 4th-order Runge-Kutta method. The numerical results are in excellent agreement with the analytical solution.

In a series of papers, Olsson (1994, 1995), Olsson & Oliger (1994), Strand (1994), Gerritsen & Olsson (1996), Yee et al. (1999a,b, 2000) and Sandham & Yee (2000), the issue of nonlinear stability of the compressible Euler and Navier-Stokes Equations, including physical boundaries, and the corresponding development of the discrete analogue of nonlinear stable high order schemes, including boundary schemes, were developed, extended and evaluated for various fluid flows. High order here refers to spatial schemes that are essentially fourth-order or higher away from shock and shear regions. The objective of this paper is to give an overview of the progress of the low dissipative high order shock-capturing schemes proposed by Yee et al. (1999a,b, 2000). This class of schemes consists of simple non-dissipative high order compact or non-compact central spatial differencings and adaptive nonlinear numerical dissipation operators to minimize the use of numerical dissipation. The amount of numerical dissipation is further minimized by applying the scheme to the entropy splitting form of the inviscid flux derivatives, and by rewriting the viscous terms to minimize odd-even decoupling before the application of the central scheme (Sandham & Yee). The efficiency and accuracy of these schemes are compared with spectral, TVD and fifth-order WENO schemes. A new approach of Sjogreen & Yee (2000) utilizing non-orthogonal multi-resolution wavelet basis functions as sensors to dynamically determine the appropriate amount of numerical dissipation to be added to the non-dissipative high order spatial scheme at each grid point will be discussed. Numerical experiments of long time integration of smooth flows, shock-turbulence interactions, direct numerical simulations of a 3-D compressible turbulent plane channel flow, and various mixing layer problems indicate that these schemes are especially suitable for practical complex problems in nonlinear aeroacoustics, rotorcraft dynamics, direct numerical simulation or large eddy simulation of compressible turbulent flows at various speeds including high-speed shock-turbulence interactions, and general long time wave propagation problems. These schemes, including entropy splitting, have also been extended to freestream preserving schemes on curvilinear moving grids for a thermally perfect gas (Vinokur & Yee 2000).

The objectives of this paper are to investigate how various numerical treatments of the nonlinear source term in a model reaction-convection equation can affect the stability of steady-state numerical solutions and to show under what conditions the conventional linearized analysis breaks down. The underlying goal is to provide part of the basic building blocks toward the ultimate goal of constructing suitable numerical schemes for hypersonic reacting flows, combustions and certain turbulence models in compressible Navier-Stokes computations. It can be shown that nonlinear analysis uncovers much of the nonlinear phenomena which linearized analysis is not capable of predicting in a model reaction-convection equation.

When a time-dependent approach is used to obtain steady-state numerical solutions of a fluid flow or a steady nonlinear partial differential equation (PDE), a boundary value problem is transformed into an initial-boundary value problem with unknown initial data. If the steady PDE is strongly nonlinear and/or contains stiff nonlinear source terms, then slow convergence, nonconvergence or spurious steady state numerical solutions can occur even though the time step is well below the CFL limit and the initial data are physically relevant. Here the term “time-dependent approach” is used loosely to include some of the iteration procedures (due to implicit time discretizations), relaxation procedures and preconditioners for convergence acceleration strategies in numerically solved steady PDEs. This is due to the fact that most of these procedures can be viewed as approximations of time-dependent PDEs. Using nonlinear dynamics and local and global bifurcation theory, much of the asymptotic behavior of the resulting nonlinear discretized counterparts from finite discretizations of model PDEs can be analyzed and explained [1–9].

In this paper certain global properties of dynamical systems governed by nonlinear difference equations are studied. When an asymptotically stable equilibrium state or periodic solution exists, it is desirable to be able to determine a global region of asymptotic stability in the state space. In this paper an effective method is presented for the determination of such a region. It will be seen that once certain features of the backward mapping have been properly delineated, the development of the method becomes a rather simple one. The method is mainly presented for second-order systems but the basic ideas are also applicable to higher-order systems. Through the development of the theory and examples, one also sees that, in general, the region of asymptotic stability for a nonlinear difference system is of extremely complex shape.

Many dynamical systems and mechanics problems are governed by nonlinear difference equations. These equations have also been used increasingly to model problems in population dynamics, economics, and ecology. In this paper we study systems governed by the nonlinear difference equation (4). The locally asymptotically stable periodic solutions are investigated and the global behavior of the system for different values of the system parameter and for different initial conditions is examined. Although the equation is a simple one, the general pattern of its solution is surprisingly complex and seems to have implications in many fields.

Magnetic resonance imaging (MRI) offers a sensitive alternative to computed tomography (CT) for lesion localization. Patients with subacute necrotizing encephalomyelopathy (SNE) may be diagnosed by finding focal lesions on CT that correspond to sites of anatomical involvement. We report serial CT and MRI scanning findings in a patient with clinical, radiographic, and laboratory evidence of SNE. MRI was more sensitive in detecting lesions involving the basal ganglia, brainstem, and cortex. We believe MRI is a valuable and sensitive means to establish an antemortem diagnosis of SNE.

The shock-capturing capability of total variation diminishing (TVD) schemes is demonstrated for a more realistic complex shock-diffraction problem for which the experimental data are available. Second-order explicit upwind and symmetric TVD schemes are used to solve the time-dependent Euler equations of gas dynamics for the interaction of a blast wave with an airfoil at high angle-of-attack. The test cases considered are a time-dependent moving curved-shock wave and a contant moving planar-shock wave impinging at an angle-of-attack 30 deg on a NACA 0018 airfoil. Good agreement is obtained between isopycnic contours computed by the TVD schemes and those from experimental interferograms. No drastic difference in flow-field structure is found between the curved- and planar-shock wave cases, except for a difference in density level near the lower surface of the airfoil. Computation for cases with higher shock Mach numbers is also possible. Numerical experiments show that the symmetric TVD scheme is less sensitive to the boundary conditions treatment than the upwind scheme.

Changes to Program Laura (Langley Aerothermodynamic Upwind Relaxation Algorithm) are presented which enhance both stability and accuracy of the algorithm. A discussion of iteration/sweeping strategies and their relation to computer architectures is included to best exploit the capabilities of serial, vector, and parallel processor machines. Test cases for Mach 10 perfect gas flow and Mach 32 real gas flow in chemical nonequilibrium over a blunt, raked elliptic cone using the thin-layer Navier-Stokes equations are presented in order to demonstrate the current improved capabilities. Algorithm changes include the use of volume averaging, application of a symmetric total variation diminishing (TVD) scheme, and stronger interaction between the grid/shock alignment routine and the relaxation algorithm. Good comparisons with heat transfer and pitching moment data at three different angles of attack for the Mach 10 tests serve to further validate the present algorithm. Parameters are defined which control the coupling of the specie continuity equations with the solution of the mixture conservation equations. A discussion of the consequences involved in the choice of strong versus weak coupling is presented, and a sample nonequilibrium calculation on a fine grid over a full scale model of the Aeroassist Flight Experiment (AFE) demonstrates current capabilities.

A semiimplicit high-resolution shock-capturing method for multidimensional systems of hyperbolic conservation laws with stiff source terms has been developed by Yee and Shinn (1987). The goal of this work is to extend this method to solve the three-dimensional fully coupled Navier-Stokes equations for a hypersonic chemically reacting flow in generalized coordinates. In this formulation, the global continuity equation was replaced by all the species continuity equations. The shock-capturing technique is a second-order-accurate, symmetric total-variation-diminishing method which accounts fully and directly for the coupling among the fluid and all the species. To verify the current approach, it was implemented into an existing computer code which contained the MacCormack method. Test results for a five-species reacting flow are shown to be oscillation-free around the shock, and the time spent per iteration only doubles when compared to the result using classical way of supplying numerical dissipation. The extra computation is more than justified by the elimination of spurious oscillation and nonlinear instability associated with the classical shock-capturing schemes in computing hypersonic reacting flows.