Analytic test cases for three-dimensional hydrodynamic models

Exact periodic solutions are generated for the 3-D hydrodynamic equations in linearized form. A linear slip condition is enforced at the bottom, based on the velocity at the bottom. It is shown that the bottom stress can be equivalently expressed in terms of the vertically averaged velocity, and expressions for this bottom stress coefficient are derived in terms of the primary parameters of the problem. As a result, the three-dimensional structure may be assembled from conventional solutions to (a) the 1-D vertical diffusion equation; and (b) the 2-D vertically averaged shallow water equations. In the latter, the bottom stress effects are shown to be complex and frequency-dependent, and an additional rotational term is required for their representation.     

A computational model for the limit analysis of three-dimensional masonry structures

This paper extends previous work on the limit analysis of ductile frames and plane masonry arches to the limit analysis of three-dimensional masonry structures. A lower-bound approach is developed which can handle three-dimensional collapse mechanisms involving any combination of sliding, twisting and hingeing at the block interfaces. A computer program for determining the collapse load of such structures is used to study (a) the equilibrium limits of a block with four contact points resting on an inclined plane and (b) the collapse of a semicircular arch of four blocks. The paper also describes experimental and computational work on a radially symmetric model dome of 380 blocks subject to foundation settlement.

---

Sommario Il presentre contributo estende al campo delle structture tridimensionali in muratura un precedente lavoro sull'analisi limite di telai duttili ed archi in muratura piani. Si e' sviluppato un approccio statico che analizza meccanismi di collasso tridimensionale ottenuti per combinazione dei meccanismi semplici di scorrimento e rotazione nel piano e fuori dal piano delle superfici di interfaccia tra i blocchi. Si descrivono (a) i limiti di equilibrio di un blocco con 4 punti di contatto su base inclinata, (b) le condizioni di collasso di un arco semicircolare costituito da quattro blocchi, applicando un programma di calcolo redatto per l'analisi e la definizione del carico di collasso di tali strutture. La terza parte dell'articolo presenta il lavoro sperimentale e di calcolo sviluppato su un modello di cupola a simmetria radiale costituita da 380 blocchi soggetta a cedimenti fondali.

     

Multiphase computational method for thermal interactions between compressible fluid and arbitrarily shaped solids

A numerical method was investigated for multiphase fields consisting of compressible gas and arbitrarily shaped solids. Since the proposed model is based on a one‐fluid model in which variables are averaged according to the phase fractions in the computational cells; it enables us to estimate gas‐solid momentum and thermal interactions without setting up adapting grids even if the solids have extremely complicated shapes. The governing equations are derived with the characteristics of an ideal gas assuming the specific heat to be uniform in the multiphase field. The derived equations in conservative form are discretized with a finite volume method. In addition, the pressure is calculated implicitly in a similar way to incompressible flow solvers. Because of these improvements, the proposed method allows us to calculate low Mach number compressible flows free from the Courant‐Friedrichs‐Lewy condition based on the speed of sound and to conserve the mass more accurately. To confirm the validity of the proposed method, it was applied to natural convection around an isothermal cylinder and a heat‐conducting pipe. In comparison with previous studies, it was confirmed that the gas flows and temperature distributions are predicted reasonably. In addition, a numerical experiment was conducted under more complicated conditions, namely, gas leaking from a container including heat sources. As a result, it was demonstrated that the proposed method enables us to predict unsteady variations of pressure and temperature distributions in the container due to the leakage while still conserving mass accurately.     

Humidity-driven bifurcation in a hydrogel-actuated nanostructure: A three-dimensional computational analysis

Hydrogel-based adaptive structures that respond to specific external stimuli present immense potential for applications in microfluidics, shape-memory devices, artificial muscle and actuators. Using a three-dimensional finite element method, we analyse the humidity-driven bifurcation of a nanostructure, made up of periodically distributed nanoscale rods embedded vertically in a swollen hydrogel layer. The bifurcation manifests as a switching behavior of the nanorods between vertical and tilted states. The use of representative volume element with realistic boundary conditions allows us to fully consider inhomogeneous deformations of the hydrogel. Our computations reveal that at higher initial swelling ratio, the bifurcation behavior of the nanostructure approaches that of the case where homogeneous deformation in the hydrogel is considered. However, large deviation in the behavior may occur between the two at lower initial swelling ratio. We further investigate quantitatively the effects of geometrical and material variations on the bifurcation behavior. It is found that geometric-material parameters can significantly affect the critical switching state and its post-bifurcation behavior, enabling great tunability in the design and application of hydrogel-based adaptive nanostructure.     

Comparison between three-dimensional linear and nonlinear tsunami generation models

The modeling of tsunami generation is an essential phase in understanding tsunamis. For tsunamis generated by underwater earthquakes, it involves the modeling of the sea bottom motion as well as the resulting motion of the water above. A comparison between various models for three-dimensional water motion, ranging from linear theory to fully nonlinear theory, is performed. It is found that for most events the linear theory is sufficient. However, in some cases, more-sophisticated theories are needed. Moreover, it is shown that the passive approach in which the seafloor deformation is simply translated to the ocean surface is not always equivalent to the active approach in which the bottom motion is taken into account, even if the deformation is supposed to be instantaneous.      

Recent developments in multiphysics computational models of physiological flows

A mini-symposium on computational modeling of fluid–structure interactions and other multiphysics in physiological flows was held at the 11th World Congress on Computational Mechanics in July 2014 in Barcelona, Spain. This special issue of Theoretical and Computational Fluid Dynamics contains papers from among the participants of the mini-symposium. The present paper provides an overview of the mini-symposium and the special issue.     

Experimental study of supersonic three-dimensional jets

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 75–80, May–June, 1988.     

Experimental and computational modeling of wave propagation in granular materials

A hybrid experimental-computational study has been conducted in order to determine the propagational characteristics of mechanical waves in granular materials. The experimental investigation has used the method of dynamic photoelasticity to collect photographic data which provide information on the wave speeds, integranular contact loadings, and wave-spreading characteristics. The computational study employed the use of the distinct-element method whereby the motion of each granule in the material is modeled by rigid-body dynamics assuming each particle interaction has particular frictionless stiffness and damping forces. The experimental results provide special dynamic material constants necessary for the computational modeling, and they also provide data for comparison purposes. Results from the experimental and computational studies compare well with each other and indicate that local microstructure plays an important role in the wave propagation through such materials.     

Experimental and computational studies of shock wave-to-bubbly water momentum transfer

Momentum transfer from shock waves (SWs) of various intensity (from 0.05 MPa to 0.5 MPa in amplitude) to water containing air bubbles 2.5 to 4 mm of mean diameter is studied both experimentally and by means of numerical simulation. Experiments are performed in a vertical shock tube of a 50 × 100 mm² rectangular cross section consisting of a 495-mm long high-pressure section (HPS), 495-mm long low-pressure section (LPS), and 990 mm long test section (TS) equipped with an air bubbler and filled with water. Experiments have shown that as the initial gas volume fraction in water increases from 0 to 0.3 the momentum imparted in bubbly water by SWs increases monotonically, gradually levelling off at an air volume fraction of about 0.30. The experimental data are confirmed by two-dimensional (2D) simulation of SW propagation in bubbly water in terms of the SW velocity versus the air content, pressure profiles, as well as liquid and gas velocity behind the shock front.     

Experimental validation of computational fluid dynamics modeling for narrow tillage tool draft

Energy requirement of a tillage tool, mostly represented by tool draft, is a function of different soil–tool interaction components like soil parameters, tool parameters and system parameters. Soil–tool interaction modeling was conducted using computational fluid dynamics (CFD) approach considering soil as a Bingham material. Soil bin tests were conducted to validate tool draft predictions obtained from this numerical modeling. Numerical predictions and soil bin experiments for the tool draft were observed with 40 mm wide vertical tool operating at four different depths of 40, 80, 120, and 160 mm. The tool was operated at four different operating speeds of 1, 8, 16 and 24 km h⁻¹ in clay loam soil with two moisture contents of 14% and 20%. Thus, the experimental design consisted in a (2 × 4 × 4) complete randomized factorial with two replications for each test. Simulation results over-predicted tool draft in comparison to the experimental values. The difference between the predicted and measured draft were not consistent and ranged from 1% to 42%, with an average of 24% and 22% for moisture contents of 14% and 20%, respectively. The agreement of simulation data with experimental values was higher at shallow depth of operation and lower tool operating speed. The correlation coefficient between the simulation and experimental draft were found to vary from 0.9275 to 0.9914.     

A stable algorithm for bed friction in three-dimensional shallow sea modal models

The mathematical formulation of a three-dimensional shallow sea model using a modal expansion in the veitical is briefly described. The importance of the time discretization of the vertical diffusion term and bottom friction term is discussed in some detail. Both stability theory and numerical calculations show the importance of time centring or evaluating the modal form of the viscosity term at the higher time step in order to develop a numerically efficient algorithm. Similar analysis and calculations show that in shallow water it is essential to time centre or evaluate bottom friction at the higher time step. In the case of linear bottom friction it is shown that this condition can be readily accomplished. However, using a quadratic friction formulation (a more physically realistic form), this cannot be readily achieved. A new algorithm is presented whereby a stable solution can be obtained even in shallow water using quadratic bottom friction.     

Faults simulations for three-dimensional reservoir-geomechanical models with the extended finite element method

Faults are geological entities with thicknesses several orders of magnitude smaller than the grid blocks typically used to discretize reservoir and/or over-under-burden geological formations. Introducing faults in a complex reservoir and/or geomechanical mesh therefore poses significant meshing difficulties. In this paper, we consider the strong-coupling of solid displacement and fluid pressure in a three-dimensional poro-mechanical (reservoir-geomechanical) model. We introduce faults in the mesh without meshing them explicitly, by using the extended finite element method (X-FEM) in which the nodes whose basis function support intersects the fault are enriched within the framework of partition of unity. For the geomechanics, the fault is treated as an internal displacement discontinuity that allows slipping to occur using a Mohr–Coulomb type criterion. For the reservoir, the fault is either an internal fluid flow conduit that allows fluid flow in the fault as well as to enter/leave the fault or is a barrier to flow (sealing fault). For internal fluid flow conduits, the continuous fluid pressure approximation admits a discontinuity in its normal derivative across the fault, whereas for an impermeable fault, the pressure approximation is discontinuous across the fault. Equal-order displacement and pressure approximations are used. Two- and three-dimensional benchmark computations are presented to verify the accuracy of the approach, and simulations are presented that reveal the influence of the rate of loading on the activation of faults.     

Experimental stress-intensity distributions in three-dimensional cracked-body problems

For over a decade, the first author and his associates have worked towards the development of an optical-experimental-modeling technique for predicting both the flaw shape and the stress-intensity-factor distribution in three-dimensional cracked-body problems where neither are knowna priori. The application is associated with subcritical flaw growth, the precursor to most service fractures. This paper presents an assessment of results obtained by applying the technique which consists of a marriage between frozen-stress photoelasticity and moiré analysis to measure the stress-intensity-factor distribution across a straight-front crack in a body of finite thickness.     

A practical implementation of turbulence models for the computation of three-dimensional separated flows

An upwind MUSCL-type implicit scheme for the three-dimensional Navier-Stokes equations is presented and details on the implementation for three-dimensional flows of a ‘diagonal’ upwind implicit operator are developed. Turbulence models for separated flows are also described with an emphasis on the numerical specificities of the Johnson-King non-equilibrium model. Good predictions of separated two- and three-dimensional flows are demonstrated.