A shock capturing scheme for steady, supercritical, free-surface flow

Abstract A finite difference scheme is presented for the solution of the two-dimensional shallow water equations in steady, supercritical flow. The scheme incorporates numerical characteristic decomposition, is shock capturing by design and incorporates space-marching as a result of the assumption that the flow is wholly supercritical in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

A TVD finite difference scheme with non-uniform meshes and without upstream weighting

We present a finite difference scheme, with the TVD (total variation diminishing) property, for scalar conservation laws. The scheme applies to non-uniform meshes, allowing for variable mesh spacing, and is without upstream weighting. When applied to systems of conservation laws, no scalar decomposition is required, nor are any artificial tuning parameters, and this leads to an efficient, robust algorithm.

Shock capturing scheme for steady, supersonic, isentropic flow

A finite difference scheme is presented for the solution of the two-dimensional equations of steady, supersonic, isentropic flow. The scheme incorporates numerical characteristic decomposition, is shock-capturing by design and incorporates space marching as a result of the assumption that the flow is wholly supersonic in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

A finite difference scheme for inviscid flows with non-eequilibrium chemistry and internal energy

A finite difference scheme is presented for the inviscid terms of the equations of compressible fluid dynamics with general non-equilibrium chemistry and internal energy.

A finite difference scheme for steady, supersonic, two-dimensional, compressible flow of real gases

A finite difference scheme is presented for the solution of the two-dimensional equations of steady, supersonic, compressible flow of real gases. The scheme incorparates numerical characteristic decomposition, is shock-capturing by design and incorporates space-marching as a result of the assumption that the flow is wholly supersonic in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

A numerical scheme for two-dimensional, open channel flows with non-rectangular geometries

An algorithm based on flux difference splitting is presented for the solution of two-dimensional, open channel flows. A transformation maps a non-rectangular, physical domain into a rectangular one. The governing equations are then the shallow water equations, including terms of slope and friction, in a generalized coordinate system. A regular mesh on a rectangular computational domain can then be employed. The resulting scheme has good jump capturing properties and the advantage of using boundary/body-fitted meshes. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

Error estimates for a fully discrete spectral scheme for a class of nonlinear, nonlocal dispersive wave equations

We analyze a fully discrete spectral method for the numerical solution of the initial- and periodic boundary-value problem for two nonlinear, nonlocal, dispersive wave equations, the Benjamin–Ono and the Intermediate Long Wave equations. The equations are discretized in space by the standard Fourier–Galerkin spectral method and in time by the explicit leap-frog scheme. For the resulting fully discrete, conditionally stable scheme we prove an L2-error bound of spectral accuracy in space and of second-order accuracy in time.

On the structure of Langmuir turbulence

The Stokes drift induced by surface waves distorts turbulence in the wind-driven mixed layer of the ocean, leading to the development of streamwise vortices, or Langmuir circulations, on a wide range of scales. We investigate the structure of the resulting Langmuir turbulence, and contrast it with the structure of shear turbulence, using rapid distortion theory (RDT) and kinematic simulation of turbulence. Firstly, these linear models show clearly why elongated streamwise vortices are produced in Langmuir turbulence, when Stokes drift tilts and stretches vertical vorticity into horizontal vorticity, whereas elongated streaky structures in streamwise velocity fluctuations (u) are produced in shear turbulence, because there is a cancellation in the streamwise vorticity equation and instead it is vertical vorticity that is amplified. Secondly, we develop scaling arguments, illustrated by analysing data from LES, that indicate that Langmuir turbulence is generated when the deformation of the turbulence by mean shear is much weaker than the deformation by the Stokes drift. These scalings motivate a quantitative RDT model of Langmuir turbulence that accounts for deformation of turbulence by Stokes drift and blocking by the air–sea interface that is shown to yield profiles of the velocity variances in good agreement with LES. The physical picture that emerges, at least in the LES, is as follows. Early in the life cycle of a Langmuir eddy initial turbulent disturbances of vertical vorticity are amplified algebraically by the Stokes drift into elongated streamwise vortices, the Langmuir eddies. The turbulence is thus in a near two-component state, with suppressed and . Near the surface, over a depth of order the integral length scale of the turbulence, the vertical velocity (w) is brought to zero by blocking of the air–sea interface. Since the turbulence is nearly two-component, this vertical energy is transferred into the spanwise fluctuations, considerably enhancing at the interface. After a time of order half the eddy decorrelation time the nonlinear processes, such as distortion by the strain field of the surrounding eddies, arrest the deformation and the Langmuir eddy decays. Presumably, Langmuir turbulence then consists of a statistically steady state of such Langmuir eddies. The analysis then provides a dynamical connection between the flow structures in LES of Langmuir turbulence and the dominant balance between Stokes production and dissipation in the turbulent kinetic energy budget, found by previous authors.

Using Doppler radar with a simple explicit microphysics model to diagnose problems with ice sublimation depth-scales in forecast models

Several previous studies have attempted to assess the sublimation depth-scales of ice particles from clouds into clear air. Upon examining the sublimation depth-scales in the Met Office Unified Model (MetUM), it was found that the MetUM has evaporation depth-scales 2–3 times larger than radar observations. Similar results can be seen in the European Centre for Medium-Range Weather Forecasts (ECMWF), Regional Atmospheric Climate Model (RACMO) and Météo-France models. In this study, we use radar simulation (converting model variables into radar observations) and one-dimensional explicit microphysics numerical modelling to test and diagnose the cause of the deep sublimation depth-scales in the forecast model. The MetUM data and parametrization scheme are used to predict terminal velocity, which can be compared with the observed Doppler velocity. This can then be used to test the hypothesis as to why the sublimation depth-scale is too large within the MetUM. Turbulence could lead to dry air entrainment and higher evaporation rates; particle density may be wrong, particle capacitance may be too high and lead to incorrect evaporation rates or the humidity within the sublimating layer may be incorrectly represented. We show that the most likely cause of deep sublimation zones is an incorrect representation of model humidity in the layer. This is tested further by using a one-dimensional explicit microphysics model, which tests the sensitivity of ice sublimation to key atmospheric variables and is capable of including sonde and radar measurements to simulate real cases. Results suggest that the MetUM grid resolution at ice cloud altitudes is not sufficient enough to maintain the sharp drop in humidity that is observed in the sublimation zone.

Minimum neighbour and extended Kalman filter estimator: a practical distributed channel assignment scheme for dense wireless local area networks

Dense deployments of wireless local area networks (WLANs) are becoming a norm in many cities around the world. However, increased interference and traffic demands can severely limit the aggregate throughput achievable unless an effective channel assignment scheme is used. In this work, a simple and effective distributed channel assignment (DCA) scheme is proposed. It is shown that in order to maximise throughput, each access point (AP) simply chooses the channel with the minimum number of active neighbour nodes (i.e. nodes associated with neighbouring APs that have packets to send). However, application of such a scheme to practice depends critically on its ability to estimate the number of neighbour nodes in each channel, for which no practical estimator has been proposed before. In view of this, an extended Kalman filter (EKF) estimator and an estimate of the number of nodes by AP are proposed. These not only provide fast and accurate estimates but can also exploit channel switching information of neighbouring APs. Extensive packet level simulation results show that the proposed minimum neighbour and EKF estimator (MINEK) scheme is highly scalable and can provide significant throughput improvement over other channel assignment schemes.

Image fusion based on median filters and SOFM neural networks: a three-step scheme

This paper presents a new image data fusion scheme by combining median filtering with self-organizing feature map (SOFM) neural networks. The scheme consists of three steps: (1) pre-processing of the images, where weighted median filtering removes part of the noise components corrupting the image, (2) pixel clustering for each image using self-organizing feature map neural networks, and (3) fusion of the images obtained in Step (2), which suppresses the residual noise components and thus further improves the image quality. It proves that such a three-step combination offers an impressive effectiveness and performance improvement, which is confirmed by simulations involving three image sensors (each of which has a different noise structure).

Orthogonal on-off BPSK: a convenient signaling scheme for near-far resistant detection in DS/CDMA

This paper proposes a convenient signaling scheme-orthogonal on-off BPSK (O3BPSK)-for near-far (NF) resistant detection in asynchronous direct-sequence code-division multiple-access (DS/CDMA) systems (uplink). The temporally adjacent bits from different users in the received signals are decoupled by using the on-off signaling, and the original data rate is maintained with no increase in transmission rate by adopting an orthogonal structure. The detector at the receiver is a one-shot linear decorrelating detector, which depends upon neither hard decision nor specific channel coding. The application of O3 strategy to the differentially encoded BPSK (D-BPSK) sequences is also presented. Finally, some computer simulations are shown to confirm the theoretical analysis.

A three-shot improvement scheme for hard-decision based linear decorrelating detector in DS/CDMA

This paper proposes a three-shot improvement scheme for the hard-decision based method (HDM), an implementation solution for linear decorrelating detector (LDD) in asynchronous DS/CDMA systems. By taking advantage of the preceding (already reconstructed) bit and the matched filter output for the following two bits, the coupling between temporally adjacent bits (TABs), which always exists for asynchronous systems, is greatly suppressed and the performance of the original HDM is substantially improved. This new scheme requires no signaling overhead yet offers nearly the same performance as those more complicated methods. Also, it can easily accommodate the change in the number of active users in the channel, as no symbol/bit grouping is involved. Finally, the influence of synchronisation errors is investigated.