Bounding Walls Research Articles

Hydrodynamic interaction between a platelet and an erythrocyte: effect of erythrocyte deformability, dynamics, and wall proximity.

We present three-dimensional numerical simulations of hydrodynamic interaction between a red blood cell (RBC) and a platelet in a wall-bounded shear flow. The dynamics and large deformation of the RBC are fully resolved in the simulations using a front-tracking method. The objective is to quantify the influence of tank treading and tumbling dynamics of the RBC, and the presence of a bounding wall on the deflection of platelet trajectories. We observe two types of interaction: A crossing event in which the platelet comes in close proximity to the RBC, rolls over it, and continues to move in the same direction; and a turning event in which the platelet turns away before coming close to the RBC. The crossing events occur when the initial lateral separation between the cells is above a critical separation, and the turning events occur when it is below the critical separation. The critical lateral separation is found to be higher during the tumbling motion than that during the tank treading. When the RBC is flowing closer to the wall than the platelet, the critical separation increases by several fold, implying the turning events have higher probability to occur than the crossing events. On the contrary, if the platelet is flowing closer to the wall than the RBC, the critical separation decreases by several folds, implying the crossing events are likely to occur. Based on the numerical results, we propose a mechanism of continual platelet drift from the RBC-rich region of the vessel towards the wall by a succession of turning and crossing events. The trajectory deflection in the crossing events is found to depend nonmonotonically on the initial lateral separation, unlike the monotonic trend observed in tracer particle deflection and in deformable sphere-sphere collision. This nonmonotonic trend is shown to be a consequence of the deformation of the RBC caused by the platelet upon collision. An estimation of the platelet diffusion coefficient yields values that are similar to those reported in experiments and computer simulations with multicellular suspension.

Electrostatic free energy for a confined nanoscale object in a fluid

We present numerical calculations of electrostatic free energies, based on the nonlinear Poisson-Boltzmann (PB) equation, for the case of an isolated spherical nano-object in an aqueous suspension, interacting with charged bounding walls. We focus on systems with a low concentration of monovalent ions (≲10(-4) M), where the range of electrostatic interactions is long (~30 nm) and comparable to the system and object dimensions (~100 nm). Locally tailoring the geometry of the boundaries creates a modulation in the object-wall interaction, which for appropriately chosen system dimensions can be strong enough to result in stable spatial trapping of a nanoscale entity. A detailed view of the underlying mechanism of the trap shows that the physics depends predominantly on counterion entropy and the depth of the potential well is effectively independent of the object's dielectric function; we further note an appreciable trap depth even for an uncharged object in the fluid. These calculations not only provide a quantitative framework for understanding geometry-driven electrostatic effects at the nanoscale, but will also aid in identifying contributions from phenomena beyond mean field PB electrostatics, e.g., Casimir and other fluctuation-driven forces.

The structure and rheology of sheared model swimmer suspensions

We analyze the rheological response of a suspension of simple model swimmers subject to a steady Couette flow. We consider the squirmer model as a means to control systematically the interplay between self-propulsion and active stress generation and analyze their relative impact both on the effective viscosity of a suspension and the microstructure the squirmers develop. We show how self-propulsion introduces an intrinsic contribution to the effective viscosity of the active suspension. Accordingly, apolar squirmers show shear thickening while polar ones develop a shear thinning response to the applied shear. We show that the detailed coupling of the squirmers to the bounding walls has a strong influence on the structure of the suspension and the development of shear bands.

Curvature-driven capillary migration and assembly of rod-like particles.

Capillarity can be used to direct anisotropic colloidal particles to precise locations and to orient them by using interface curvature as an applied field. We show this in experiments in which the shape of the interface is molded by pinning to vertical pillars of different cross-sections. These interfaces present well-defined curvature fields that orient and steer particles along complex trajectories. Trajectories and orientations are predicted by a theoretical model in which capillary forces and torques are related to Gaussian curvature gradients and angular deviations from principal directions of curvature. Interface curvature diverges near sharp boundaries, similar to an electric field near a pointed conductor. We exploit this feature to induce migration and assembly at preferred locations, and to create complex structures. We also report a repulsive interaction, in which microparticles move away from planar bounding walls along curvature gradient contours. These phenomena should be widely useful in the directed assembly of micro- and nanoparticles with potential application in the fabrication of materials with tunable mechanical or electronic properties, in emulsion production, and in encapsulation.

Thermal Assessment of Forced Convection Through Metal Foam Heat Exchangers

Using a thermal resistance approach, forced convection heat transfer through metal foam heat exchangers is studied theoretically. The complex microstructure of metal foams is modeled as a matrix of interconnected solid ligaments forming simple cubic arrays of cylinders. The geometrical parameters are evaluated from existing correlations in the literature with the exception of ligament diameter which is calculated from a compact relationship offered in the present study. The proposed, simple but accurate, thermal resistance model considers: the conduction inside the solid ligaments, the interfacial convection heat transfer, and convection heat transfer to (or from) the solid bounding walls. The present model makes it possible to conduct a parametric study. Based on the generated results, it is observed that the heat transfer rate from the heated plate has a direct relationship with the foam pore per inch (PPI) and solidity. Furthermore, it is noted that increasing the height of the metal foam layer augments the overall heat transfer rate; however, the increment is not linear. Results obtained from the proposed model were successfully compared with experimental data found in the literature for rectangular and tubular metal foam heat exchangers.

Molecular free path distribution in rarefied gases

We present the results of investigations into the distribution of molecular free paths in rarefied gases using molecular dynamics simulations. Our tests on a range of different gas densities and confinements (unbounded, single bounding wall and parallel bounding walls) indicate that the molecules perform Lévy-type flights, irrespective of the presence of a bounding wall. The free paths most closely follow a power-law distribution. Simulations of gases confined by planar surfaces indicate that the local molecular mean free path varies sharply close to a solid surface. These results may yield new insight into diffusive transport in rarefied gases, in particular, the constitutive behaviour of gas flows in micro- and nanoscale devices.

Hydrothermal circulation within the Endeavour Segment, Juan de Fuca Ridge

Areas of the seafloor at mid‐ocean ridges where hydrothermal vents discharge are easily recognized by the dramatic biological, physical, and chemical processes that characterize such sites. Locations where seawater flows into the seafloor to recharge hydrothermal cells within the crustal reservoir are by contrast almost invisible but can be indirectly identified by a systematic grid of conductive heat flow measurements. An array of conductive heat flow stations in the Endeavour axial valley of the Juan de Fuca Ridge has identified recharge zones that appear to represent a nested system of fluid circulation paths. At the scale of an axial rift valley, conductive heat flow data indicate a general cross‐valley fluid flow, where seawater enters the shallow subsurface crustal reservoir at the eastern wall of the Endeavour axial valley and undergoes a kilometer of horizontal transit beneath the valley floor, finally exiting as warm hydrothermal fluid discharge on the western valley bounding wall. Recharge zones also have been identified as located within an annular ring of very cold seafloor around the large Main Endeavour Hydrothermal Field, with seawater inflow occurring within faults that surround the fluid discharge sites. These conductive heat flow data are consistent with previous models where high‐temperature fluid circulation cells beneath large hydrothermal vent fields may be composed of narrow vertical cylinders. Subsurface fluid circulation on the Endeavour Segment occurs at various crustal depths in three distinct modes: (1) general east to west flow across the entire valley floor, (2) in narrow cylinders that penetrate deeply to high‐temperature heat sources, and (3) supplying low‐temperature diffuse vents where seawater is entrained into the shallow uppermost crust by the adjacent high‐temperature cylindrical systems. The systematic array of conductive heat flow measurements over the axial valley floor averaged ∼150 mW/m2, suggesting that only about 3% of the total energy flux of ocean crustal formation is removed by conductive heat transfer, with the remainder being dissipated to overlying seawater by fluid advection.

Conformal contour dynamics in bounded domains

A contour dynamics algorithm is presented for vortex patches in unbounded domains and in simply connected bounded domains. It is based on conformal mapping and spectral analysis. The inside and outside of a vortex patch are analytically mapped onto the inside and outside of the unit circles of two different complex planes. The flow field is determined by matching the inner and outer flows on the patch boundary. Following the Legras and Zeitlin conformal dynamics concept, the time evolution of the patch boundary is expressed by means of the time derivatives of the mapping functions. The presence of a bounding wall, which can be permeable and movable, is considered. The geometry and dynamics of the patch and the flow velocity on the bounding wall are represented by Fourier series; by assuming their coefficients as control parameters, the proposed formulation can be appealing for optimization and control purposes. Two numerical examples of the proposed technique are presented.

The velocity and shape of convected elongated liquid drops in narrow gaps

The motion and shape of a liquid drop through another continuous liquid phase (conveying phase) in a Hele-Shaw cell with two different apertures were investigated experimentally. Eight different liquid–liquid systems were tested. In all cases, the continuous phase was more viscous and wetted the bounding walls. In the capillarity-dominated region, the irregular shape of the discontinuous phase changed with time and distance, with much lower velocity than that of the conveying phase. At higher capillary number, three different shapes of stabilized elongated drops were observed. The conditions that lead to the appearance of stabilized elongated drops are discussed. In contrast to gas–liquid systems, the velocity of these stabilized elongated drops was 2 to 4.7 times higher than that of conveying liquid. Two new correlations are derived from dimensionless analysis and the experimental data to predict the elongated drop shape and velocity as a function of the dimensionless parameters governing the system.

The Velocity and Shape of Convected Elongated Liquid Drops in Vertical Narrow Gaps

Abstract The motion and shape of a liquid drop through another continuous liquid phase (conveying phase) in a vertical Hele-Shaw cell with two different apertures were investigated experimentally. Two different liquid/liquid systems were tested. In all cases, the continuous phase was more viscous and wetted the bounding walls. In the capillarity-dominated region, the irregular shape of the discontinuous phase changed with time and distance, with much lower velocity than that of the conveying phase. In contrast to gas/liquid systems, the velocity of these stabilized, elongated drops was 2.5 to almost 5 times higher than that of conveying liquid. Despite the similarities between flow in vertical and horizontal Hele-Shaw cells, the velocity of droplets in a vertical fracture is different from that of a horizontal fracture. A new correlation is derived from dimensionless analysis and the experimental data to predict the elongated drop velocity as a function of the dimensionless parameters governing the system. Introduction Two-phase flow in micro-fractures is fundamental to many different fields of advanced science and technology, such as chemical process engineering, bioengineering, medical and genetic engineering, as well as petroleum engineering. For instance, understanding the flow of two-phase fluids in near-parallel gaps through fractured rocks has a significant effect on design of different recovery methods for naturally fractured reservoir. The flow pattern of two-phase immiscible flow in a fracture depends on the flow rates of the phases, the geometry, aperture, roughness of the fracture, the flow properties of the phases and interfacial tension between the phases. The flow patterns in a fracture are different from that in macro-sized rectangular ducts or pipes because of the small aperture, which can enhance capillary effects. The flow structure in the fracture affects the flow and transport through the surrounding porous matrix blocks. The slug flow pattern in a fracture, which occurs over a wide range of parameters, is frequently encountered in oil-wet fractured reservoirs during the immiscible displacement of viscous oil. It also occurs in natural gas reservoirs during displacement of water during gas production.

Investigation and visualization of liquid–liquid flow in a vertically mounted Hele-Shaw cell: flow regimes, velocity and shape of droplets

The motion and shape of a liquid drop flowing within a continuous, conveying liquid phase in a vertical Hele-Shaw cell were investigated experimentally. The continuous phase was more viscous and wetted the bounding walls of the Hele-Shaw cell. The gap between the Hele-Shaw plates was set equal to 0.0226 cm. Four different flow regimes were observed: (a) small-droplet flow, (b) elongated-droplet flow, (c) churn flow and (d) channel flow. At low capillary number, that is, when capillary forces are larger than viscous forces, the droplet shape was irregular and changed with time and distance, and it moved with lower velocity than that of the conveying phase. At higher capillary number, several different shapes of stabilized elongated and flattened drops were observed. In contrast to gas–liquid systems, the velocities of droplets are higher than that of conveying liquid. New correlations derived from dimensionless analysis and fitted to the experimental data were generated to predict the elongated-drop velocity and aspect ratio.

Effects of wall compliance on the linear stability of Taylor–Couette flow

The stability of the laminar flow in the narrow gap between infinitely long concentric cylinders, the inner of which rotates, is examined for the case of compliant bounding walls, modelled as thin cylindrical shells supported by rigid frames through arrays of springs and dampers. Sufficiently soft walls have a destabilizing influence on the axisymmetric Taylor vortices produced by the centrifugal force, although the effect is limited to modes with large axial wavelengths. Due to the walls flexibility, hydroelastic modes are generated. Complex modal exchanges are observed, as function of the wall properties and the Reynolds number. For axisymmetric modes an asymptotic analysis is conducted in the limit of small axial wavenumber, to show the correspondence between such exchanges and singularities in the analytical solutions. While the axisymmetric modes dominate the spectrum when the walls are rigid or very mildly compliant, a critical non-zero azimuthal wavenumber exists for which the hydroelastic modes become more unstable. Shorter azimuthal waves are favoured by increasing spring stiffness.

The effect of sidewalls on rectangular jets

An experimental study is presented regarding the influence of sidewalls on the turbulent free jet flow issuing from a smoothly contracting rectangular nozzle of aspect ratio 15. “Sidewalls” are two parallel plates, flush with each of the slots’ short sides, practically establishing bounding walls extending the nozzle sidewalls in the downstream direction. Measurements of the streamwise and lateral velocity mean and turbulent characteristics have been accomplished, with an x-sensor hot wire anemometer, up to an axial distance of 35 nozzle widths, for jets with identical inlet conditions with and without sidewalls. Centreline measurements for both configurations have been collected for three Reynolds numbers, Re D = 10,000, 20,000 and 30,000. For Re D = 20,000 measurements in the transverse direction were collected at 13 different downstream locations in the range, x = 0–35 nozzle widths, and in the spanwise direction at three different downstream locations, x = 2, 6 and 25 nozzle widths. Results indicate that, the two jet configurations (with and without sidewalls) produce statistically different flow fields. Sidewalls do not lead to the production of a 2D flow field as undulations in the spanwise mean velocity distribution indicate. They do increase the two-dimensionality of the jet increasing the longevity of 2D spanwise rollers structures formed in the initial stages of entrainment, which are responsible for the convection of longitudinal momentum towards the outer field, establishing larger streamwise mean velocities at the jet edges. In the near field, up to 25 nozzle widths, lower outward lateral velocities in the presence of the sidewalls are held responsible for the decrease of turbulent terms including rms of velocity fluctuations and Reynolds stresses. Skewness factors increase monotonically across the shear layers from negative values to positive forming sharp peaks at the outer edges of the jet, illustrative of the presence of well defined 2D roller structures in the jet with sidewalls.

Evaluation of Turbulence Models for External Flows

An industry-motivated investigation of the application of turbulence models to external fluid flows has been carried out. The motivating application is the melt-blowing fiber production process used by 3M in which friction forces exerted by high-speed air jets stretch pliable polymeric fibers. The complex fluid flow is turbulent and unique. The closest traditional fluid flow is the wall jet. In order to achieve results of sufficient accuracy to be used in the design of the production equipment, a necessary prerequisite is the identification of an appropriate turbulence model. To this end, five turbulence models, commonly offered in commercially available CFD software (FLUENT® Software, ANSYS® CFX® Software, and Star-CD™ Software) were carefully implemented in appropriate numerical simulations of the available experimental data. The investigated turbulence representations included several two-equation models and a direct solution of the RANS equation. The experimental data consisted of measured velocity profiles for the plane wall jet and the cylindrical wall jet. A comparison of the velocity profiles extracted from the simulations with those of experiment enabled a clear conclusion to be drawn about the most suitable turbulence model, which was found to be the standard k − ϵ model with enhanced near-wall treatment. For all the simulations, the accuracy of the numerical simulations was carefully investigated with respect to three critical issues: number of control volumes, deployment of the control volumes, and the geometry and the extent of the solution domain. The deployment issue is of great significance in the neighborhood of a bounding wall and directly influences the near-wall treatment. The choice of the solution domain controls the boundary conditions and the surfaces at which they are applied. A general conclusion that follows from this study is that it is essential to verify the suitability of a turbulence model before applying it to real-world applications.

The Art of Apple Peeling

The Art of Apple Peeling Janice N. Harrington (bio) 1 A child stands in the kitchen of a one bedroom flat watching as her mother flays apples with a blade no longer than an index finger, paring apples while the pressure cooker’s valve turns this way round and that way back again to spit its hiss of steam. On the counter, beside the stove, in a metal wash pan, apples lie banked and glowing like embers, like lanterns lifted by a mother’s steady hands. Unfazed by brilliance or heat, she trims their skins into scrolls, into scrim, thin, thin, till the peels slip and spiral into her child’s cupped hands. Curled from her knife’s lathe, there turns a red road, a red flag, the apple’s red tongue singing of sweetness, of shape and boundary. 2 An apple turned and turning, centered in a woman’s palm, the cut and the wound, the knife pushed between pulp and peel, the skin slowly shaved and slipped away—this is the art of apple peeling. This is seduction and revelation that begins with wounding. The peel winds round, spiraling, a moment into other moments, sliding as a silk robe slides from a woman’s shoulder. The light that shines upon her bare skin is not the sun, but the beloved who watches. The light that shines is her nakedness. She is a colored woman. She shines. She shines apple bright. 3 In a kitchen in Wichita Falls, in a one bedroom flat, in ‘58 or ‘59, there is a child. She watches her mother. The child is colored. The mother is yellow. They have not yet removed their skins, nor will they. [End Page 1076] But the child draws between her lips her mother’s gift, a ribbon, a well rope, a red string for a kite, an umbilical cord, a helix coiling the way one thought coils around another, a screwing spill like molasses from a biscuit sop or spittle from slack lips. In the palm of a yellow woman an apple lies plump as the Grande Odalisque. An apple sits plump and smooth-skinned and shining upon a couch of flesh. An apple’s peeling is a curtain, a caul, a bounding wall. What lies hidden beneath an apple’s skin? Is desire the gnawing worm or the worm bitten? Is it the worm-heart curled in a womb of flesh or is it the apple heart that teaches dimension: the death-worm that feeds unseen in what is, at first, sweet, at first, for us alone, at first, safe? But it doesn’t matter. The mother will stab out the worm and worm-corrupted parts and pitch the leavings into the pressure cooker, lesson learned. 4 Api Toile, Carpentin; Foxwhelp, Sturmer; Tremlett’s Bitter, Gilpin; Hauxapfel, Dulcet; Early Joe, Anna; Lady in the Snow, Toko; Leather Coat, Mutsu; Walter Please, Billie Bound; Alexander, and Seek-To-Further. 5 Will you ever taste a Shiawassee? 6 If I say the sun hangs like a Tallow Pippin, if I say its light is autumn cider or white vinegar, if I say a heartbeat is the low note of windfall apples, if I say there are more varieties of apples than of love, or if I say love resembles the slow art of apple peeling—requiring attention, a sharp edge, a wound, revelation, and a falling away, if I say the word of God is written not on a brittle scroll but on an apple peeling, if the sum of all darkness is no bigger than an apple seed, and an apple’s white meat is the sum of all light, [End Page 1077] if I say the moon is only a peeled apple, the stars a glittery peel reeled into nebulae and constellation, if I say I know this because I am Eve’s daughter and have pressed an unpeeled apple against my thigh, if I say I am the slayer of apples, have sucked apple peelings like the entrails of the sacrifice, have seen the death-worm and bitten it and swallowed but remember only the apple’s sweetness, if I say these words and hold...

Unified Treatment of Natural Convection in Tall Narrow and Flat Wide Rectangular Enclosures

Numerical simulation was used to investigate natural convection in rectangular enclosures ranging in aspect ratio from tall, narrow shapes to flat, wide shapes. For each of the selected aspect ratios, the Rayleigh number was varied over a range of approximately four decades. Two fundamental thermal boundary conditions were considered. One of these, commonly designed as heating from below, involved the imposition of a temperature at the lower bounding wall that is higher than that at the upper bounding wall. The side walls of the enclosure were maintained adiabatic for this case. The second employed boundary condition was side walls at different uniform temperatures and adiabatic upper and lower boundaries. For each aspect ratio and for both types of boundary conditions, the onset of natural convection from the regime of pure conduction occurred at a definitive value of the Rayleigh number, termed the critical Rayleigh number. Once that threshold value was exceeded, the Nusselt number increased markedly with increasing Rayleigh number, the sharpness of the increase being greater for the bottom-heated case. For that case and for aspect ratios (height/width) greater than one, the breakdown of a flow pattern characterized by a single recirculation zone caused a sudden halt to the increase of the Nusselt number. This breakdown was followed by a rapid reformation of the flow pattern into a pair of recirculation zones, one situated above the other. The critical Rayleigh number was insensitive to the aspect ratio for flat, wide enclosures but, on the contrary, the critical value increased markedly with increasing aspect ratio for tall, narrow enclosures. In general, a critical Rayleigh number for the bottom-heated case exceeded that for the side-heated case by a factor of 12.

Influence of Torque on the Lift and Drag of a Particle in an Oscillatory Flow

In the work of Fischer et al. (2002, “Forces on Particles in an Oscillatory Boundary Layer,” J. Fluid Mech., 468, pp. 327–347, 2005; “Influence of Wall Proximity on the Lift and Drag of a Particle in an Oscillatory Flow,” ASME J. Fluids Eng., 127, pp. 583–594) we computed the lift and drag forces on a sphere, subjected to a wall-bounded oscillatory flow. The forces were found as a function of the Reynolds number, the forcing frequency, and the gap between the particle and the ideally smooth rigid bounding wall. Here we investigate how the forces change as a function of the above parameters and its moment of inertia if the particle is allowed to freely rotate. Allowing the particle to rotate does not change appreciably the drag force, as compared to the drag experienced by the particle when it is held fixed. Lift differences between the rotating and nonrotating cases are shown to be primarily dominated in the mean by the pressure component. The lift of the rotating particle varies significantly from the fixed-particle case and depends strongly on the Reynolds number, the forcing frequency, and the gap; much less so on the moment of inertia. Of special significance is that the lift is enhanced for small Reynolds numbers and suppressed for larger ones, with a clear transition point. We also examine how the torque changes when the particle is allowed to rotate as compared to when it is held fixed. As a function of the Reynolds number the torque of the fixed sphere is monotonically decreasing in the range Re=5 to Re=400. The rotating-sphere counterpart experiences a smaller and more complex torque, synchronized with the lift transition mentioned before. As a function of the gap, the torque is significantly larger in the fixed particle case.

Platelet Adhesive Dynamics. Part I: Characterization of Platelet Hydrodynamic Collisions and Wall Effects

Abnormally high shear stresses encountered in vivo induce spontaneous activation of blood platelets and formation of aggregates, even in the absence of vascular injury. A three-dimensional multiscale computational model—platelet adhesive dynamics—is developed and applied in Part I and Part II articles to elucidate key biophysical aspects of GPIb α-von-Willebrand-factor-mediated interplatelet binding that characterizes the onset of shear-induced platelet aggregation. In this article, the hydrodynamic effects of the oblate spheroidal shape of platelets and proximity of a plane wall on the nature of cell-cell collisions are systematically investigated. Physical quantities characterizing the adhesion probabilities between colliding platelet surfaces for the entire range of near-wall encounters between two platelets are obtained for application in platelet adhesive dynamics simulations of platelet aggregation explored in a companion article. The technique for matching simulation predictions of interplatelet binding efficiency to experimentally determined efficiencies is also described. Platelet collision behavior is found to be strikingly different from that of spheres, both close to and far from a bounding wall. Our results convey the significant effects that particle shape and presence of a bounding wall have on the particle trajectories and collision mechanisms, collision characteristics such as collision time and contact area, and collision frequency.

Dynamics of surfactant‐covered drops in linear flows

AbstractSurfactants modify interfacial properties and significantly affect drop behavior in flow. We study the dynamics of a drop, which is covered with a monolayer of insoluble surfactant, in linear viscous flows, both unbounded and in the presence of a wall. The effect of viscosity contrast is included. Analytical results in a form of expansions for weak flows and high viscosity drops are developed. Numerical results with three‐dimensional boundary integral simulations are used to explore large deformations. The results show that surfactant generally enhances drop deformation, certainly under small‐deformation conditions. The steady‐state drop shape and surfactant distribution are independent of viscosity contrast in straining flows (e.g. hyperbolic, axisymmetric strain). The drop shape and surfactant distribution are insensitive to viscosity contrast under small deformation conditions for any linear flow; the effect of the rotational component at higher‐order. The theory quantifies the effect of surfactant on drop migration away from a bounding wall as well as the rheology of dilute emulsions. It predicts non‐Newtonian features such as shear thinning viscosity and normal stress. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

An improved transmission line matrix model for the 2D ideal wedge benchmark problem

The numerical modelling of acoustic propagation in underwater environments using transmission line matrix (TLM) has received little attention for some time. This has been due, in part, to the need for an open boundary description, also known as a ‘perfectly matched load’ or PML, and the requirement for an accurate description of non-uniform bounding walls. The first of these problems has been solved by many researchers in subsequent years. The paper describes a novel solution to the second problem, allowing the incorporation of boundary-conforming Cartesian meshes into TLM schemes for acoustic propagation. This and a related technique are compared using the Buckingham and Tolstoy ideal 2D wedge benchmark test.