Two-dimensional similarity between forms I and II of cytenamide, a carbamazepine analogue

Cytenamide form I (R (3) over bar) undergoes a solid-state transformation upon heating to form II (P (1) over bar), with the structures exhibiting the same two-dimensional similarity that exists between the R (3) over bar and P (1) over bar forms of carbamazepine.

Approximate Riemann solutions of the two-dimensional shallow-water equations

A finite-difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow-water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gasdynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. An extension to the two-dimensional equations with source terms, is included. The scheme is applied to a dam-break problem with cylindrical symmetry.

An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gas dynamics is defined, and a scheme, based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem, and incorporates the technique of operator splitting. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. An extension to the two-dimensional equations with source terms is included. The scheme is applied to the one-dimensional problems of a breaking dam and reflection of a bore, and in each case the approximate solution is compared to the exact solution of ideal fluid flow. The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section. Finally, the scheme is applied to two other dam-break problems, this time in two dimensions with one having cylindrical symmetry. Each approximate solution compares well with those given by other authors.

Solutions of a two-dimensional dam-break problem

Solutions of a two-dimensional dam break problem are presented for two tailwater/reservoir height ratios. The numerical scheme used is an extension of one previously given by the author [J. Hyd. Res. 26(3), 293–306 (1988)], and is based on numerical characteristic decomposition. Thus approximate solutions are obtained via linearised problems, and the method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations.

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.

Riemann solvers with primitive parameter vectors for two-dimensional compressible flows of a real gas

An analysis of averaging procedures is presented for an approximate Riemann solver for the equations governing the compressible flow of a real gas. This study extends earlier work for the Euler equations with ideal gases.

Switching on a two-dimensional time-harmonic scalar wave in the presence of a diffracting edge

This paper concerns the switching on of two-dimensional time-harmonic scalar waves. We first review the switch-on problem for a point source in free space, then proceed to analyse the analogous problem for the diffraction of a plane wave by a half-line (the ‘Sommerfeld problem’), determining in both cases the conditions under which the field is well-approximated by the solution of the corresponding frequency domain problem. In both cases the rate of convergence to the frequency domain solution is found to be dependent on the strength of the singularity on the leading wavefront. In the case of plane wave diffraction at grazing incidence the frequency domain solution is immediately attained along the shadow boundary after the arrival of the leading wavefront. The case of non-grazing incidence is also considered.

Dynamic stall for a Vertical Axis Wind Turbine in a two-dimensional study

The last few years have proved that Vertical Axis Wind Turbines (VAWTs) are more suitable for urban areas than Horizontal Axis Wind Turbines (HAWTs). To date, very little has been published in this area to assess good performance and lifetime of VAWTs either in open or urban areas. At low tip speed ratios (TSRs<5), VAWTs are subjected to a phenomenon called 'dynamic stall'. This can really affect the fatigue life of a VAWT if it is not well understood. The purpose of this paper is to investigate how CFD is able to simulate the dynamic stall for 2-D flow around VAWT blades. During the numerical simulations different turbulence models were used and compared with the data available on the subject. In this numerical analysis the Shear Stress Transport (SST) turbulence model seems to predict the dynamic stall better than the other turbulence models available. The limitations of the study are that the simulations are based on a 2-D case with constant wind and rotational speeds instead of considering a 3-D case with variable wind speeds. This approach was necessary for having a numerical analysis at low computational cost and time. Consequently, in the future it is strongly suggested to develop a more sophisticated model that is a more realistic simulation of a dynamic stall in a three-dimensional VAWT.