A non-uniform mesh scheme for compressible flow

A non-uniform mesh scheme is presented for the computation of compressible flows governed by the Euler equations of gas dynamics. The scheme is based on flux-difference splitting and represents an extension of a similar scheme designed for uniform meshes. The numerical results demonstrate that little, if any, spurious oscillation occurs as a result of the non-uniformity of the mesh; and importantly, shock speeds are computed correctly.

Shallow water flow with cylindrical symmetry

A numerical scheme is presented tor the solution of the shallow water equations in a single radial coordinate. This can prove useful when testing codes for the two-dimensional shallow water equations. The scheme is applied with success to problems involving converging and diverging bores.

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 Riemann solver for compressible flow of a real gas in a Lagrangian frame

An approximate Riemann solver is presented for the compressible flow equations with a general (convex) equation of state in a Lagrangian frame of reference.

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.

An isentropic flow algorithm with body fitted meshes

An efficient algorithm based on flux difference splitting is presented for the solution of the three-dimensional equations of isentropic flow in a generalised coordinate system, and with a general convex gas law. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The algorithm requires only one function evaluation of the gas law in each computational cell. The scheme has good shock capturing properties and the advantage of using body-fitted meshes. Numerical results are shown for Mach 3 flow of air past a circular cylinder. Furthermore, the algorithm also applies to shallow water flows by employing the familiar gas dynamics analogy.

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.

Prediction of supercritical flow in open channels

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow water equations in open channels. 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. 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. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

Structure of single-wall peptide nanotubes: in situ flow aligning X-ray diffraction

The structure of single wall peptide nanotubes is presented for the model surfactant-like peptide A6K. Capillary flow alignment of a sample in the nematic phase at high concentration in water leads to oriented X-ray diffraction patterns. Analysis of these, accompanied by molecular dynamics simulations, suggests the favourable self-assembly of antiparallel peptide dimers into beta-sheet ribbons that wrap helically to form the nanotube wall.

Small-angle x-ray scattering study of flow alignment of a thermotropic liquid crystal in the nematic and smectic phases

WThe capillary flow alignment of the thermotropic liquid crystal 4-n-octyl-4′-cyanobiphenyl in the nematic and smectic phases is investigated using time-resolved synchrotron small-angle x-ray scattering. Samples were cooled from the isotropic phase to erase prior orientation. Upon cooling through the nematic phase under Poiseuille flow in a circular capillary, a transition from the alignment of mesogens along the flow direction to the alignment of layers along the flow direction (mesogens perpendicular to flow) appears to occur continuously at the cooling rate applied. The transition is centered on a temperature at which the Leslie viscosity coefficient α3 changes sign. The configuration with layers aligned along the flow direction is also observed in the smectic phase. The transition in the nematic phase on cooling has previously been ascribed to an aligning-nonaligning or tumbling transition. At high flow rates there is evidence for tumbling around an average alignment of layers along the flow direction. At lower flow rates this orientation is more clearly defined. The layer alignment is ascribed to surface-induced ordering propagating into the bulk of the capillary, an observation supported by the parallel alignment of layers observed for a static sample at low temperatures in the nematic phase.

Flow-induced dynamic surface tension effects at nanoscale

The aim of this study is to investigate flow-induced dynamic surface tension effects, similar to the well-known Marangoni phenomena, but solely generated by the nanoscale topography of the substrates. The flow-induced surface tension effects are examined on the basis of a sharp interface theory. It is demonstrated how nanoscale objects placed at the boundary of the flow domain result in the generation of substantial surface forces acting on the bulk flow.

Liquid flow over a substrate structured by seeded nanoparticles

Recent experiments have demonstrated that nanoparticles which sparsely distributed over a solid substrate can substantially change the flow conditions at the solid surface in the presence of slip. Inspired by these observations, the flow past tiny particles seeded on a solid substrate is investigated theoretically in the framework of an interface formation model. It has been shown, that even a single seeded nanoparticle can reduce significantly the measurable tangential component of hydrodynamic velocity at the substrate and affect the amount of the observed apparent slippage of the liquid. The effect from the particle manifests in a form of a long relaxation tail defined by the characteristic time of the interface formation process. A comparison with experiments has demonstrated a good agreement between theoretically predicted and experimentally observed values of the relaxation tail length scale.

Credit flow [poetry]

A poem within the Alhambra Poetry Calendar 2011, a desk calendar and poetry anthology in one.