Upwind Bias Research Articles

Temporal novelty detection and multiple timescale integration drive Drosophila orientation dynamics in temporally diverse olfactory environments.

To survive, insects must effectively navigate odor plumes to their source. In natural plumes, turbulent winds break up smooth odor regions into disconnected patches, so navigators encounter brief bursts of odor interrupted by bouts of clean air. The timing of these encounters plays a critical role in navigation, determining the direction, rate, and magnitude of insects' orientation and speed dynamics. Disambiguating the specific role of odor timing from other cues, such as spatial structure, is challenging due to natural correlations between plumes' temporal and spatial features. Here, we use optogenetics to isolate temporal features of odor signals, examining how the frequency and duration of odor encounters shape the navigational decisions of freely-walking Drosophila. We find that fly angular velocity depends on signal frequency and intermittency-the fraction of time signal can be detected-but not directly on durations. Rather than switching strategies when signal statistics change, flies smoothly transition between signal regimes, by combining an odor offset response with a frequency-dependent novelty-like response. In the latter, flies are more likely to turn in response to each odor hit only when the hits are sparse. Finally, the upwind bias of individual turns relies on a filtering scheme with two distinct timescales, allowing rapid and sustained responses in a variety of signal statistics. A quantitative model incorporating these ingredients recapitulates fly orientation dynamics across a wide range of environments and shows that temporal novelty detection, when combined with odor motion detection, enhances odor plume navigation.

A Finite Volume Upwind-Biased Centred Scheme for Hyperbolic Systems of Conservation Laws: Application to Shallow Water Equations

AbstractWe construct a new first-order central-upwind numerical method for solving systems of hyperbolic equations in conservative form. It applies in multidimensional structured and unstructured meshes. The proposed method is an extension of the UFORCE method developed by Stecca, Siviglia and Toro, in which the upwind bias for the modification of the staggered mesh is evaluated taking into account the smallest and largest wave of the entire Riemann fan. The proposed first-order method is shown to be identical to the Godunov upwind method in applications to a 2 x 2 linear hyperbolic system. The method is then extended to non-linear systems and its performance is assessed by solving the two-dimensional inviscid shallow water equations. Extension to second-order accuracy is carried out using an ADER-WENO approach in the finite volume framework on unstructured meshes. Finally, numerical comparison with current competing numerical methods enables us to identify the salient features of the proposed method.

Directional Diffusion Regulator (DDR) for some numerical solvers of hyperbolic conservation laws

A computational tool called “Directional Diffusion Regulator (DDR)” is proposed to bring forth real multidimensional physics into the upwind discretization in some numerical schemes of hyperbolic conservation laws. The direction based regulator when used with dimension splitting solvers, is set to moderate the excess multidimensional diffusion and hence cause genuine multidimensional upwinding like effect. The basic idea of this regulator driven method is to retain a full upwind scheme across local discontinuities, with the upwind bias decreasing smoothly to a minimum in the farthest direction. The discontinuous solutions are quantified as gradients and the regulator parameter across a typical finite volume interface or a finite difference interpolation point is formulated based on fractional local maximum gradient in any of the weak solution flow variables (say density, pressure, temperature, Mach number or even wave velocity etc.). DDR is applied to both the non-convective as well as whole unsplit dissipative flux terms of some numerical schemes, mainly of Local Lax–Friedrichs, to solve some benchmark problems describing inviscid compressible flow, shallow water dynamics and magneto-hydrodynamics. The first order solutions consistently improved depending on the extent of grid non-alignment to discontinuities, with the major influence due to regulation of non-convective diffusion. The application is also experimented on schemes such as Roe, Jameson–Schmidt–Turkel and some second order accurate methods. The consistent improvement in accuracy either at moderate or marked levels, for a variety of problems and with increasing grid size, reasonably indicate a scope for DDR as a regular tool to impart genuine multidimensional upwinding effect in a simpler framework.

Upwind-biased FORCE schemes with applications to free-surface shallow flows

In this paper we develop numerical fluxes of the centred type for one-step schemes in conservative form for solving general systems of conservation laws in multiple-space dimensions on structured meshes. The proposed method is an extension of the multidimensional FORCE flux developed by Toro et al. (2009) [14]. Here we introduce upwind bias by modifying the shape of the staggered mesh of the original FORCE method. The upwind bias is evaluated using an estimate of the largest eigenvalue, which in any case is needed for selecting a time step. The resulting basic flux is first-order accurate and monotone. For the linear advection equation, the proposed UFORCE method reproduces exactly the upwind Godunov method. Extension to non-linear systems has been done empirically via the two-dimensional inviscid shallow water equations. Second order of accuracy in space and time on structured meshes is obtained in the framework of finite volume methods. The proposed method improves the accuracy of the solution for small Courant numbers and intermediate waves associated with linearly degenerate fields (contact discontinuities, shear waves and material interfaces). It achieves comparable accuracy to that of upwind methods with approximate Riemann solvers, though retaining the simplicity and efficiency of centred methods. The performance of the schemes is assessed on a suite of test problems for the two-dimensional shallow water equations.

A new interface‐capturing discretization scheme for numerical solution of the volume fraction equation in two‐phase flows

AbstractA new high‐resolution spatial discretization scheme for use with the interface‐capturing volume‐of‐fluid method is presented and applied to several test cases. The new scheme is intended to preserve the volume fraction discontinuity without the need to explicitly reconstruct the interface within computational control volumes near the interface. The method is based on maximization of the volume fraction gradient in the region of the interface, while stability is preserved by maintaining net upwind biasing of the face flux prescription in each computational control volume. In addition, the scheme employs face limiting to satisfy boundedness criteria at finite‐volume control surfaces (faces) and prevent variable overshoot. The method has been developed for use with unstructured, anisotropic, and/or inhomogeneous meshes that are often used for simulation of geometrically complex flow fields. This paper presents the implementation of the new discretization scheme into a steady‐state solver in order to isolate the spatial discretization from the time integration technique. The new scheme is validated for steady‐state two‐phase flow using several test cases, and is shown to preserve the phase interface almost exactly, with essentially zero dissipative or dispersive error in the volume fraction solution. Copyright © 2008 John Wiley & Sons, Ltd.

A generalization of the Runge–Kutta iteration

Iterative solvers in combination with multi-grid have been used extensively to solve large algebraic systems. One of the best known is the Runge–Kutta iteration. We show that a generally used formulation [A. Jameson, Numerical solution of the Euler equations for compressible inviscid fluids, in: F. Angrand, A. Dervieux, J.A. Désidéri, R. Glowinski (Eds.), Numerical Methods for the Euler Equations of Fluid Dynamics, SIAM, Philadelphia, 1985, pp. 199–245] does not allow to form all possible polynomial transmittance functions and we propose a new formulation to remedy this, without using an excessive number of coefficients. After having converted the optimal parameters found in previous studies (e.g. [B. Van Leer, C.H. Tai, K.G. Powell, Design of optimally smoothing multi-stage schemes for the Euler equations, AIAA Paper 89–1923, 1989]) we compare them with those that we obtain when we optimize for an integrated 2-grid V -cycle and show that this results in superior performance using a low number of stages. We also propose a variant of our new formulation that roughly follows the idea of the Martinelli–Jameson scheme [A. Jameson, Analysis and design of numerical schemes for gas dynamics 1, artificial diffusion, upwind biasing, limiter and their effect on multigrid convergence, Int. J. Comput. Fluid Dyn. 4 (1995) 171–218; J.V. Lassaline, Optimal multistage relaxation coefficients for multigrid flow solvers. http://www.ryerson.ca/~jvl/papers/cfd2005.pdf] used on the advection–diffusion equation which that can be extended to other types. Gains in the order of 30%–50% have been shown with respect to classical iterative schemes on the advection equation. Better results were also obtained on the advection–diffusion equation than with the Martinelli–Jameson coefficients, but with less than half the number of matrix-vector multiplications.

Direct numerical simulation of turbulent spots

A group of high-order finite-difference schemes for incompressible flow was implemented to simulate the evolution of turbulent spots in channel flows. The long-time accuracy of these schemes was tested by comparing the evolution of small disturbances to a plane channel flow against the growth rate predicted by linear theory. When the perturbation is the unstable eigenfunction at a Reynolds number of 7500, the solution grows only if there are a comparatively large number of (equispaced) grid points across the channel. Fifth-order upwind biasing of convection terms is found to be worse than second-order central differencing. But, for a decaying mode at a Reynolds number of 1000, about a fourth of the points suffice to obtain the correct decay rate. We show that this is due to the comparatively high gradients in the unstable eigenfunction near the walls. So, high-wave-number dissipation of the high-order upwind biasing degrades the solution especially. But for a well-resolved calculation, the weak dissipation does not degrade solutions even over the very long times (O(100)) computed in these tests. Some new solutions of spot evolution in Couette flows with pressure gradients are presented. The approach to self-similarity at long times can be seen readily in contour plots.

A naturally upwinded conservative procedure for the incompressible Navier-Stokes equations on non-staggered grids

Upwind methods have been previously adopted in incompressible flow calculations in an attempt to eliminate the need for artificial viscosity while maintaining high accuracy. Standard upwind methods found in the literature are primarily concerned with accurate modeling of the convection terms and generally neglect the viscous terms in the analysis. A new procedure is developed here which seeks to include the viscous terms so that regions of significant gradients will not be over-dissipated. The approach taken here is an extension of the work of Refs [1–5]in which interpolating functions are derived from direct integration of linearized forms of the governing equations. The resulting functions are then used as interpolants for differencing the full equations. During the process, no attempt is made to deliberately upwind bias the differencing. However, because of the manner in which coefficients of the differencing are functions of the cell Reynolds number, the scheme introduces its own upwind bias. This property was first observed by Roscoe [1] in which the observation that this class of schemes preserves the hyperbolic/elliptic nature of the original system of equations was made. The present work yields, for the first time, a fully conservative Roscoe-type method. Although the method approaches the development of the finite difference equations in a different manner than traditional upwind procedures, it achieves higher accuracy in a manner analogous to the MUSCL approach [6] used in standard upwind schemes. The procedure also uses a unique discretization of the continuity equation which involves pressure terms as in Ref. [5]. This equation is fully conservative and satisfies mass conservation to machine zero. The new scheme is first demonstrated on the 1-D, viscous, Burger's equation and results are compared with a first and second-order Roe scheme. It is then applied to the 2-D, incompressible Navier-Stokes equations for non-staggered grids. Results for the driven cavity problem are compared with proven methods and are found to be in excellent agreement.

Upwind flight of tsetse (Glossina spp.) in response to natural and synthetic host odour in the field

Abstract. In Zimbabwe, studies were made of the flight responses of tsetse (Glossina spp.) to synthetic and natural ox odour using arrangements of electric nets.Tsetse flying away from a target showed a significant upwind bias when a blend of carbon dioxide (2/1 min), acetone (500 mg/h), octenol (0.4 mg/h), 4‐methylphenol (0.8 mg/h) and 3‐n‐propylphenol (0.1 ma) was dispensed 15 m upwind, with c. 35% flying upwind.Without carbon dioxide this percentage was significantly reduced to 15% which was not significantly different from that with no odour (8%).This pattern was not altered by reducing the doses of acetone, octenol and phenols by 10–100 times, to levels comparable to those produced by an ox.With natural ox odour or a synthetic equivalent of ox odour dispensed from a ventilated pit 8 m upwind of the target, c. 28% flew upwind.This was reduced significantly to 15% if carbon dioxide was removed.In studies using a 17 m line of nets arranged orthogonally across the prevailing wind line, c. 50% of the catch was caught on the downwind side in the absence of odour.This increased significantly to c.60% when acetone, octenol and phenols were dispensed 15 m upwind, with or without carbon dioxide.With a shorter line (9 m) or an incomplete one (16.5 m long with 5 times 1.5 m wide gaps along its length) there was no change in the proportion caught downwind.For all three lines, dispensing odour upwind increased the catch 2–5 times on both the up‐and downwind sides of the nets.It is concluded that a stronger upwind response to host odour is elicited when carbon dioxide is present.It is suggested that in nature upwind flight is very imprecisely orientated, with tsetse making flights up and down an odour plume ‘searching’ for a host.

Simulation of quantum transport in memory-switching double-barrier quantum-well diodes.

Recent experiments on GaAs/AlAs double-barrier diodes incorporating ${\mathit{n}}^{\mathrm{\ensuremath{-}}}$/${\mathit{n}}^{+}$/${\mathit{n}}^{\mathrm{\ensuremath{-}}}$ spacer layers have shown that they exhibit two conduction curves that remain distinct across zero bias. Such devices can be reversibly switched between the two conduction curves and retain memory of the curve last switched to, even after short-circuit conditions. In this paper, we model the memory-switching phenomenon using a quantum kinetic formulation based on the Wigner distribution function. To obtain accurate Wigner distribution functions, an improved four-point difference scheme with an upwind bias is used to model the drift term in the equation of motion. The calculations result in two equilibrium (zero-voltage) states in double-barrier diodes incorporating ${\mathit{n}}^{\mathrm{\ensuremath{-}}}$/${\mathit{n}}^{+}$/${\mathit{n}}^{\mathrm{\ensuremath{-}}}$ spacer layers. Associated with each equilibrium state is a distinct and stable conduction curve. This work is a step toward an understanding of the more complex aspects of the phenomenon, such as state switching when the device is driven far from equilibrium.

An Upwind Nodal Integral Method for Incompressible Fluid Flow

An upwind nodal solution method is developed for the steady, two-dimensional flow of an incompressible fluid. The formulation is based on the nodal integral method, which uses transverse integrations, analytical solutions of the one-dimensional averaged equations, and node-averaged uniqueness constraints to derive the discretized nodal equations. The derivation introduces an exponential upwind bias by retaining the streamwise convection term in the homogeneous part of the transverse-integrated convection-diffusion equation. The method is adapted to the stream function-vorticity form of the Navier-Stokes equations, which are solved over a nonstaggered nodal mesh. A special nodal scheme is used for the Poisson stream function equation to properly account for the exponentially varying vorticity source. Rigorous expressions for the velocity components and the no-slip vorticity boundary condition are derived from the stream function formulation.The method is validated with several benchmark problems. An idealized purely convective flow of a scalar step function indicates that the nodal approximation errors are primarily dispersive, not dissipative, in nature. Results for idealized and actual recirculating driven-cavity flows reveal a significant reduction in false diffusion compared with conventional finite difference techniques.

Orientation of tsetse flies to wind, within and outside host odour plumes in the field

Abstract Free‐flying wild tsetse flies (Glossina pallidipes Aust. and G. m. morsitans Westw.) were video recorded in Zimbabwe as they flew within an artificial host odour plume at 3, 7 or 15 m from the source, or in no odour, with and without a 0.75 m2 vertical, black visual target present aligned with the wind. With no visual target present, flights in odour were strongly biased upwind, and in the absence of odour strongly biased downwind. With the target present, between 16% and 40% of the upwind approaching flies responded visually as they passed the target, by circling it, in proportion to the proximity of the source (taken to be proportional to the mean odour concentration). Crosswind approaching flies (for whom the target will have been visible for some metres away) circled more frequently (34–56%), but without obvious correlation with the odour concentration. Circling flies also responded orthokinetically, by slowing down as they passed the target. The departure directions relative to the wind of flies leaving the target were significantly affected by the odour concentration. At 3 m they left the target in all directions, except possibly avoiding due upwind. At 7 m they left with an obliquely upwind bias, but at 15 m and also in no odour, they left with a strong crosswind bias.

The host‐orientated behaviour of tsetse flies (Glossina): the interaction of visual and olfactory stimuli

ABSTRACT. Studies were made in Zimbabwe of the propensity of Glossina pallidipes Austen and G. morsitans morsitans Westwood to divert from flying upwind in plumes of host odour to various visual features (termed targets). Using various arrangements of electrocuting nets with targets placed downwind of an odour source it was found that 45% diverted to a square target, c. 30% diverted to a black vertical oblong and there was no significant diversion to a bark‐coloured vertical oblong that simulated the bole of a tree. The relative propensity of tsetse to divert to variously coloured targets decreased in the order: black = blue > red > yellow; for different shapes it decreased in the order: circle > square > horizontal oblong = vertical oblong. Changes in the composition or concentration of the odour, or loss of contact with it, did not markedly affect the percentage that diverted. Tsetse that diverted to a target and subsequently flew away from it showed an upwind bias in the presence of odour. In the absence of odour there was a slight crosswind bias. If these crosswind fliers then flew into a plume of host odour they turned c. 50d̀ upwind.

The flight and landing of tsetse (Glossina) in response to components of host odour in the field

ABSTRACT. Studies were conducted in Zimbabwe of the responses of Glossina morsitans morsitans Westwood and Glossina pallidipes Austen to various host odours using either arrangements of electrocuting nets or visual observations. Tsetse flying upwind in a plume of carbon dioxide, acetone and octenol turned downwind upon flying into a plume of acetone or octenol, but did not turn upon flying into a plume of carbon dioxide. They also turned in response to a transient decline in odour concentration. Tsetse landed on the ground in the vicinity of a source of natural odour or artificial odour containing carbon dioxide but not at sources of acetone or octenol only. The proportion of female G.pallidipes caught at a source of natural odour (37%) was significantly different from that caught at a source of synthetic odour (17%). Resting tsetse stimulated by natural odour took off sooner than non‐stimulated flies and had a strong upwind bias in the direction of take off. Tsetse stimulated with artificial odour did not take off sooner than non‐stimulated flies. It is suggested that there is an unidentified components) of ox odour that activates resting tsetse.

Conditions for the construction of multi-point total variation diminishing difference schemes

Conditions are derived for the construction of total variation diminishing difference schemes with multi-point support. These conditions, which are proved for explicit, implicit, and semi-discrete schemes, correspond in a general sense to the introduction of upwind biasing.

二次元翼列を過ぎる遷音速ポテンシャル流のＡＦ１法による計算

A method is presented for calculating the flowfield about a cascade of arbitrary two-dimensional blades. A conformal transformation is used to generate a finite-difference grid. Implicit approximate factorization (AF) scheme is used for the solution of matrix equations resulting from finite-difference approximation to the full potential equation in conservation form. For transonic flows, an artificial viscosity, required to maintain stability in supersonic regions, is introduced by an upwind bias of the density. This allows the simple matrix form of the schevie to be retained over the entire flowfield. Supercritical test cases are considered. Blade Mach number or pressure distributions have been computed and are in good agreement with independent results.

Conservative full-potential calculations for axisymmetric, transonicflow

A conservative, finite-difference, full-potential relaxation code has been developed to solve transonic flow around axisymmetric or nonlifting, planar, two-dimensional bodies. The program utilizes the artificial compressibility method to provide an upwind bias in supersonic regions. Calculated examples include a wide variety of axisymmetric and planar two-dimensional shapes with various blunt, pointed and open ends in subsonic, transonic, and low supersonic free streams. Comparisons between conservative and nonconservative full-potential calculations show perfect agreement at convergence when the flow is entirely subsonic. Noticeable differences exist, however, between the conservative and nonconservative solutions for transonic flows with shocks.

Discrete Weighted Mean Approximation of a Model Convection-Diffusion Equation

Five-point finite-difference approximations are considered for a model (linear, constant-coefficient) convection-diffusion equation in two dimensions. Standard difference schemes for such problems behave badly when the convective terms are dominant. A new discretization is derived from a local integral representation of the true solution. This derivation is analogous to the way that the discrete Laplacian can be derived from the mean-value property of harmonic functions, and it generalizes an approach due to Allen and Southwell [Quart. J. Mech. Appl. Math., 8 (1955), pp. 129–45]. Also discussed is how the strong upwind bias of this and other discretizations serves to make more stable some methods of the two-sweep or marching type for the direct solution of the resulting linear algebraic equations.

A Strongly Implicit Procedure for Steady Three-Dimensional Transonic Potential Flows

A rapid relaxation algorithm for the numerical solution of the conservative full potential equation is described and used to predict transonic potential flow past thick swept wings. A sheared parabolic coordinate system is used to simplify the treatment of boundary conditions and an upwind bias is applied to the density in supersonic regions. A unique feature of the present work is the extension of a strongly implicit procedure, that has, in the past, been applied only to elliptic equations, to the present elliptic-hyperbolic problem. Numerical results are presented to demonstrate that the present method is considerably faster than existing line relaxation procedures.

Fast, Conservative Algorithm for Solving the Transonic Full-Potential Equation

A fast, fully implicit approximate factorization algorithm designed to solve the conservative, transonic, full-potential equation in either two or three dimensions is described. The algorithm uses an upwind bias of the density coefficient for stability in supersonic regions. This provides an effective upwind difference of the streamwise terms for any orientation of the velocity vector (i.e., rotated differencing), thereby greatly enhancing the reliability of the present algorithm. A numerical transformation is used to establish an arbitrary body-fitted, finite-difference mesh. Computed results for both airfoils and simplified wings demonstrate substantial improvement in convergence speed for the new algorithm relative to standard successive-line over-relaxation algorithms.