Multiple level finite element analysis and its applications to tidal current flow in Tokyo Bay

A finite element method for the analysis of a one level and a multiple level current flow is presented. The basic equations can be derived from the three-dimensional Navier-Stokes equations under the shallow water assumptions. The standard finite element method has been introduced using the linear interpolation function based on a triangular finite element. For each level, the finite element subdivisions are not required to be coincident. To integrate the discretized equations numerically in time, an improved two step explicit scheme is employed. The multiple level finite element method is applied to a tidal flow analysis of Tokyo Bay.The multiple level tidal flow analysis is performed at the entrance channel of Tokyo Bay. The density of water is assumed to be constant for each level. The vertical profiles of the numerical velocity are compared with those of the observed velocity. The flow directions and the order of velocity are both well in agreement with the observed data. The tidal flow pattern in Tokyo Bay has been shown to be expressed by the multiple level flow assuming that the density of seawater is levelwise constant.The numerical tidal flow computation of Tokyo Bay carried out using a one level model is compared with observed data. The one level numerical values will be used to specify the boundary conditions for the multiple level analysis. Both numerical and observed results correspond extremely well in this computation. The two dominant circulated residual flows have been computed, and they coincide with the observed facts.     

An Iterative Method for the Poisson Equation and Its Multiprocessor Implementation

An iterative multiprocessor method is proposed and implemented for solving the Poisson equation for problems in two- and three-dimensional spatial settings. The method is applied to simulate 3D fluid-dynamic flow in a cavity. The flow is simulated using a system of quasi-hydrodynamic equations. The calculation results are compared with the literature. Parallelization is found to be highly efficient.     

Motorway traffic parameter estimation from mobile phone counts

In this paper a new method for real time estimation of vehicular flows and densities on motorways is proposed. This method is based on fusing traffic counts with mobile phone counts. The procedure used for the estimation of traffic flow parameters is based on the hypothesis that “instrumented” vehicles can be counted on specific motorway sections and traffic flow can be measured on entrance and exit ramps. The motorway is subdivided into cells, assuming that mobile phones entering and exiting every cell can be counted during the observation period. An estimate of “instrumented” vehicle concentration is obtained and propagated on the network in time and space. This allows one to estimate traffic flow parameters by sampling “instrumented” traffic flow parameters using a “concentration” (the ratio of the densities of instrumented vehicles to the density of overall traffic) propagation mechanism.     

Network flow assignment as a fixed point problem

This paper deals with the user equilibrium problem (flow assignment with equal journey time by alternative routes) and system optimum (flow assignment with minimal average journey time) in a network consisting of parallel routes with a single origin-destination pair. The travel time is simulated by arbitrary smooth nondecreasing functions. We prove that the equilibrium and optimal assignment problems for such a network can be reduced to the fixed point problem expressed explicitly. A simple iterative method of finding equilibriumand optimal flow assignment is developed. The method is proved to converge geometrically; under some fairly natural conditions the method is proved to converge quadratically.     

Mathematical modeling and numerical simulation of two-phase flows using Fourier pseudospectral and front-tracking methods: The proposition of a new method

In the present work, an extension of the Fourier Pseudospectral Method coupled with the Immersed Boudary Method for non-periodic problems (IMERSPEC) applied to numerical simulation of two-phase flow was developed. The proposed method was originally developed for single-phase, incompressible flow. Here, the method is extended to two-phase flows using the front-tracking method (IMERSPEC-FT) to model fluid-fluid interfaces. The proposed method was verified and validated through results involving spurious currents, mass conservation and numerical experiments analysis for rising bubbles. IMERSPEC-FT is shown to be a promising scheme for the two-phase computational fluid dynamics (CFD).     

Space-time discontinuous Galerkin method for the solution of fluid-structure interaction

The paper is concerned with the application of the space-time discontinuous Galerkin method (STDGM) to the numerical solution of the interaction of a compressible flow and an elastic structure. The flow is described by the system of compressible Navier-Stokes equations written in the conservative form. They are coupled with the dynamic elasticity system of equations describing the deformation of the elastic body, induced by the aerodynamical force on the interface between the gas and the elastic structure. The domain occupied by the fluid depends on time. It is taken into account in the Navier-Stokes equations rewritten with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. The resulting coupled system is discretized by the STDGM using piecewise polynomial approximations of the sought solution both in space and time. The developed method can be applied to the solution of the compressible flow for a wide range of Mach numbers and Reynolds numbers. For the simulation of elastic deformations two models are used: the linear elasticity model and the nonlinear neo-Hookean model. The main goal is to show the robustness and applicability of the method to the simulation of the air flow in a simplified model of human vocal tract and the flow induced vocal folds vibrations. It will also be shown that in this case the linear elasticity model is not adequate and it is necessary to apply the nonlinear model.     

Modeling incompressible flows using a finite particle method

This paper describes the applications of a finite particle method (FPM) to modeling incompressible flow problems. FPM is a meshfree particle method in which the approximation of a field variable and its derivatives can be simultaneously obtained through solving a pointwise matrix equation. A set of basis functions is employed to obtain the coefficient matrix through a sequence of transformations. The finite particle method can be used to discretize the Navier–Stokes equation that governs fluid flows. The incompressible flows are modeled as slightly compressible via specially selected equations of state. Four numerical examples including the classic Poiseuille flow, Couette flow, shear driven cavity and a dam collapsing problem are presented with comparisons to other sources. The numerical examples demonstrate that FPM is a very attractive alternative for simulating incompressible flows, especially those with free surfaces, moving interfaces or deformable boundaries.     

Theorie zur Berechnung des Abströmwinkels bei Turbinengittern

Summary A simple method is given for the approximate calculation of the outlet flow angle for cascades of narrow-spaced blades of the type used in steam and gas turbines. The method is based on continuity and momentum equation and may be applied to compressible flow.      

A Hybrid Immersed Interface Method for Driven Stokes Flow in an Elastic Tube

We present a hybrid numerical method for simulating fluid flow through a compliant, closed tube, driven by an internal source and sink. Fluid is assumed to be highly viscous with its motion described by Stokes flow. Model geometry is assumed to be axisymmetric, and the governing equations are implemented in axisymmetric cylindrical coordinates, which capture 3D flow dynamics with only 2D computations. We solve the model equations using a hybrid approach: we decompose the pressure and velocity fields into parts due to the surface forcings and due to the source and sink, with each part handled separately by means of an appropriate method. Because the singularly-supported surface forcings yield an unsmooth solution, that part of the solution is computed using the immersed interface method. Jump conditions are derived for the axisymmetric cylindrical coordinates. The velocity due to the source and sink is calculated along the tubular surface using boundary integrals. Numerical results are presented that indicate second-order accuracy of the method.     

Exact-gradient shape optimization of a 2-D Euler flow

The optimization of an obstacle shape immersed in an Eulerian flow is investigated. In order to construct a descent method, we consider the differentiation of the flow solution with respect to the shape. In the continous case, the Hadamard variational formula yields the formal derivatives. In the discrete case, we choose an upwind method with flux splitting, and proved that an exact gradient can be derived using the adjoint state. The behavior of a gradient method is studied for a family of nozzle flows.     

Python framework for hp-adaptive discontinuous Galerkin methods for two-phase flow in porous media

In this paper we present a framework for solving two-phase flow problems in porous media. The discretization is based on a Discontinuous Galerkin method and includes local grid adaptivity and local choice of polynomial degree. The method is implemented using the new Python frontend Dune-FemPy to the open source framework Dune. The code used for the simulations is made available as Jupyter notebook and can be used through a Docker container. We present a number of time stepping approaches ranging from a classical IMPES method to a fully coupled implicit scheme. The implementation of the discretization is very flexible allowing to test different formulations of the two-phase flow model and adaptation strategies.     

Transient modelling of flow distribution in automotive catalytic converters

The transient catalytic converter performance is governed by complex interactions between exhaust gas flow and the monolithic structure of the catalytic converter. Therefore, during typical operating conditions of interest, one has to take into account the effect of the inlet diffuser on the flow field at the entrance. Computational fluid dynamics (CFD) is a powerful tool for calculating the flow field inside the catalytic converter. Radial velocity profiles, obtained by a commercial CFD code, present very good agreement with respective experimental results published in the literature. However the applicability of CFD for transient simulations is limited by the high CPU demands.The present study proposes an alternative computational method for the prediction of transient flow fields in axi-symmetric converters time-efficiently. The method is based on the use of equivalent flow resistances to simulate the flow paths in the inlet and outlet catalyst sections. The proposed flow resistance modelling (FRM) method is validated against the results of CFD predictions over a wide range of operating conditions. Apart from the apparent CPU advantages, the proposed methodology can be readily coupled with already available transient models for the chemical reactions in the catalyst. A transient model for heat transfer inside the monolith is presented. An example of coupling between FRM and transient heat transfer inside the converter is included. This example illustrates the effect of flow distribution in the thermal response of a catalytic converter, during the critical phase of catalytic converter warm-up.     

A boundary integral formulation for elastically deformable particles in a viscous fluid

This paper reports a formulation and implementation of a mixed (both direct and indirect) boundary element method using the double layer and its adjoint in a form suitable for solving Stokes flow problems involving elastically deformable particles. The formulation is essentially the Completed Double Layer Boundary Element Method for solving an exterior traction problem for the surrounding fluid or solid phase, followed by an interior displacement, and a mobility problem (if required) for the elastic particles. At the heart of the method is a deflation procedure that allows iterative solution strategies to be adopted, effectively opens the way for large-scale simulations of suspensions of deformable particles to be performed. Several problems are considered, to illustrate and benchmark the method. In particular, an analytical solution for an elastic sphere in an elongational flow is derived. The stresslet calculations for an elastic sphere in shear and elongational flows indicate that elasticity of the inclusions can potentially lead to positive second normal stress difference in shear flow, and an increase in the tensile resistance in elongational flow.This work is supported by a grant from the Australian Research Grant Council. X-J F wishes to acknowledge the support of the National Natural Science Foundation of China.     

A graphical method for valuing switching options

This paper introduces a graphical method for valuing options on real asset investments that allow the investor to switch between different operating modes at a single point-in-time. The technique uses mixtures of truncated exponential functions to approximate both the probability density function for project value and the expressions for option value of each alternative. The distribution for project value is transformed into an expected cash flow function for the option under each mode of operation. After determining an optimal exercise strategy, these functions are used to determine the option value. The graphical method allows the option exercise strategy to be communicated effectively through a graphical representation of the expected cash flow functions. A comparison of this approach to the existing binomial lattice method is presented. The efficiency of the graphical method is comparable to the binomial lattice and in some cases accurate solutions can be obtained with less CPU time.     

A comparison of adaptive time stepping methods for coupled flow and deformation modeling

Many subsurface reservoirs compact or subside due to production-induced pressure changes. Numerical simulation of this compaction process is important for predicting and preventing well-failure in deforming hydrocarbon reservoirs. However, development of sophisticated numerical simulators for coupled fluid flow and mechanical deformation modeling requires a considerable manpower investment. This development time can be shortened by loosely coupling pre-existing flow and deformation codes via an interface. These codes have an additional advantage over fully-coupled simulators in that fewer flow and mechanics time steps need to be taken to achieve a desired solution accuracy. Specifically, the length of time before a mechanics step is taken can be adapted to the rate of change in output parameters (pressure or displacement) for the particular application problem being studied. Comparing two adaptive methods (the local error method—a variant of Runge–Kutta–Fehlberg for solving ode’s—and the pore pressure method) to a constant step size scheme illustrates the considerable cost savings of adaptive time stepping for loose coupling. The methods are tested on a simple loosely-coupled simulator modeling single-phase flow and linear elastic deformation. For the Terzaghi consolidation problem, the local error method achieves similar accuracy to the constant step size solution with only one third as many mechanics solves. The pore pressure method is an inexpensive adaptive method whose behavior closely follows the physics of the problem. The local error method, while a more general technique and therefore more expensive per time step, is able to achieve excellent solution accuracy overall.     

Numerical investigation of blood flow. Part I: In microvessel bifurcations

In some diseases there is a focal pattern of velocity in regions of bifurcation, and thus the dynamics of bifurcation has been investigated in this work. A computational model of blood flow through branching geometries has been used to investigate the influence of bifurcation on blood flow distribution. The flow analysis applies the time-dependent, three-dimensional, incompressible Navier–Stokes equations for Newtonian fluids. The governing equations of mass and momentum conservation were solved to calculate the pressure and velocity fields. Movement of blood flow from an arteriole to a venule via a capillary has been simulated using the volume of fluid (VOF) method. The proposed simulation method would be a useful tool in understanding the hydrodynamics of blood flow where the interaction between the RBC deformation and blood flow movement is important. Discrete particle simulation has been used to simulate the blood flow in a bifurcation with solid and fluid particles. The fluid particle method allows for modeling the plasma as a particle ensemble, where each particle represents a collective unit of fluid, which is defined by its mass, moment of inertia, and translational and angular momenta. These kinds of simulations open a new way for modeling the dynamics of complex, viscoelastic fluids at the micro-scale, where both liquid and solid phases are treated with discrete particles.     

Maximum-likelihood adjoint-state finite-element estimation of groundwater parameters under steady- and nonsteady-state conditions

A method is presented for estimating the hydraulic parameters of groundwater flow models under steady- and nonsteady-state conditions. The estimation problem is posed in the framework of maximum-likelihood theory by means of a log-likelihood criterion that includes prior estimates of the parameters. To allow for an incomplete knowledge of the covariances of the prior head and parameter errors, these covariances are expressed in terms of a few unknown statistical parameters that may be estimated jointly with the hydraulic parameters. Computational efficiency is achieved by evaluating the gradient of the estimation criterion with an adjoint-state finite-element scheme and using a combination of conjugate-gradient algorithms, coupled with Newton's method for determining the step size to be taken at each iteration. Model structure identification criteria developed in the time-series literature (all of which utilize the maximum-likelihood concept) are shown to be useful for selecting the best way to parametrize a groundwater flow region when a number of alternative schemes of parametrization are given. The paper also demonstrates the potential utility of the proposed estimation method for the optimum design of space-time measurement networks. A case study dealing with three-dimensional flow in a multiaquifer system is briefly discussed.     

An immersed-boundary method for compressible viscous flows and its application in the gas-kinetic BGK scheme

An immersed-boundary (IB) method is proposed and applied in the gas-kinetic BGK scheme to simulate incompressible and compressible viscous flows with complex stationary and moving boundaries on stationary Cartesian grids. In this method the ghost-cell technique is used to satisfy the boundary condition on the immersed boundary. A novel idea, “local boundary determination”, is put forward to identify the ghost cells, each of which may have several different ghost-cell constructions corresponding to different boundary segments. Thus, the singular behavior of the ghost cell is eliminated. Furthermore, the so-called “fresh-cell” problem that occurs when implementing the IB method in a moving-boundary simulation is resolved by a simple temporal extrapolation. The method is first applied in the gas-kinetic BGK scheme to simulate the Taylor–Couette flow, wherein the second-order spatial accuracy of the method is validated and the “super-convergence” of the BGK scheme is observed. After that the flow between a circular cylinder and a square cylinder is used as a test case to showcase the advantage of this method in resolving the singularity problem. Then the supersonic flow around a stationary cylinder, the incompressible flow around an oscillating cylinder and the compressible flow around a moving airfoil are simulated to verify that this method can be used to simulate compressible flows and handle moving boundaries. These numerical tests demonstrate the good performance of the proposed immersed-boundary method for the study of incompressible/compressible flow problems with complex stationary/moving boundaries.     

Impedance eduction from energy dissipation measurements with flow

An optimization method for the calculation of the wall impedance of a perforate from measurements under grazing flow conditions is presented. It is in particular characterized by the simultaneous eduction of the parameter set defining the impedance as function of frequency, which allows interpolation and extrapolation. The Extended Helmholtz Resonator is applied as impedance model and the simultaneous eduction is performed using a time–domain CAA method. Furthermore, the method uses processed energy data from experiments to define the objective function. The results give an insight in the effect of bias flow on the wall impedance under grazing flow conditions. It proves to be an important acoustic design parameter. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vortex generated fluid flows in multiply connected domains

A fluid flow in a multiply connected domain generated by an arbitrary number of point vortices is considered. A stream function for this flow is constructed as a limit of a certain functional sequence using the method of images. The convergence of this sequence is discussed, and the speed of convergence is determined explicitly. The presented formulas allow for an easy computation of the values of the stream function with arbitrary precision in the case of well-separated cylinders. The considered problem is important for applications such as eddy flows in oceans. Moreover, since finding the stream function of the flow is essentially identical to finding the modified Green’s function for Laplace’s equation, the presented method can be applied to a more general class of applied problems which involve solving the Dirichlet problem for Laplace’s equation.