Showing papers on "Boundary value problem published in 1996"

On pressure and velocity flow boundary conditions and bounceback for the lattice Boltzmann BGK model

Abstract: Pressure (density) and velocity boundary conditions inside a flow domain are studied for 2-D and 3-D lattice Boltzmann BGK models (LBGK) and a new method to specify these conditions are proposed. These conditions are constructed in consistency of the wall boundary condition based on an idea of bounceback of non-equilibrium distribution. When these conditions are used together with the improved incompressible LBGK model by Zou et al., the simulation results recover the analytical solution of the plane Poiseuille flow driven by pressure (density) difference with machine accuracy. Since the half-way wall bounceback boundary condition is very easy to implement and was shown theoretically to give second-order accuracy for the 2-D Poiseuille flow with forcing, it is used with pressure (density) inlet/outlet conditions proposed in this paper and in Chen et al. to study the 2-D Poiseuille flow and the 3-D square duct flow. The numerical results are approximately second-order accurate. The magnitude of the error of the half-way wall bounceback is comparable with that using some other published boundary conditions. Besides, the bounceback condition has a much better stability behavior than that of other boundary conditions.

Numerical Approximation of Hyperbolic Systems of Conservation Laws

Abstract: From the contents: Introduction: Definitions and Examples.- Nonlinear hyperbolic systems in one space dimension.- Gas dynamics and reaction flows.- Finite Difference Schemes for one-dimensional systems.- The case of multidimensional systems.- An Introduction to Boundary conditions.

Global uniqueness for a two-dimensional inverse boundary value problem

Abstract: We show that the coefficient -y(x) of the elliptic equation Vie (QyVu) = 0 in a two-dimensional domain is uniquely determined by the corresponding Dirichlet-to-Neumann map on the boundary, and give a reconstruction pro

The tanh method: I. Exact solutions of nonlinear evolution and wave equations

Abstract: A systemized version of the tanh method is used to solve particular evolution and wave equations. If one deals with conservative systems, one seeks travelling wave solutions in the form of a finite series in tanh. If present, boundary conditions are implemented in this expansion. The associated velocity can then be determined a priori, provided the solution vanishes at infinity. Hence, exact closed form solutions can be obtained easily in various cases.

Artificial boundaries and flux and pressure conditions for the incompressible navier–stokes equations

Abstract: Fluid dynamical problems are often conceptualized in unbounded domains. However, most methods of numerical simulation then require a truncation of the conceptual domain to a bounded one, thereby introducing artificial boundaries. Here we analyse out experience in choosing artificial boundary conditions implicitly through the choice of variational formulations. We deal particularly with a class of problems that involve the prescription of pressure drops and/or net flux conditions.

Perfectly matched layers for elastodynamics: a new absorbing boundary condition

Abstract: The use of perfectly matched layers (PML) has recently been introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. In this paper, we will first prove that a fictitious elastodynamic material half-space exists that will absorb an incident wave for all angles and all frequencies. Moreover, the wave is attenuative in the second half-space. As a consequence, layers of such material could be designed at the edge of a computer simulation region to absorb outgoing waves. Since this is a material ABC, only one set of computer codes is needed to simulate an open region. Hence, it is easy to parallelize such codes on multiprocessor computers. For instance, it is easy to program massively parallel computers on the SIMD (single instruction multiple data) mode for such codes. We will show two- and three-dimensional computer simulations of the PML for the linearized equations of elastodynamics. Comparison with Liao’s ABC will be given.

Molecular dynamics simulations of a fully hydrated dipalmitoylphosphatidylcholine bilayer with different macroscopic boundary conditions and parameters

Abstract: We compared molecular dynamics simulations of a bilayer of 128 fully hydrated phospholipid (DPPC) molecules, using different parameters and macroscopic boundary conditions. The same system was studied under constant pressure, constant volume, and constant surface tension boundary conditions, with two different sets of charges, the single point charge (SPC) and extended single point charge (SPC/E) water model and two different sets of Lennard‐Jones parameters for the interaction between water and methyl/methylene. Some selected properties of the resulting bilayer systems are compared to each other, previous simulations, and experimental data. It is concluded that in relatively high water concentration it is possible to use ab initio derived charges with constant pressure boundary conditions. The SPC water model gives a larger area per head group and a broader interface than the SPC/E model. Increasing the repulsion between water oxygens and CH2/CH3 groups has a large effect on the width of the interface an...

On boundary conditions in lattice Boltzmann methods

Abstract: A lattice Boltzmann boundary condition for simulation of fluid flow using simple extrapolation is proposed. Numerical simulations, including two‐dimensional Poiseuille flow, unsteady Couette flow, lid‐driven square cavity flow, and flow over a column of cylinders for a range of Reynolds numbers, are carried out, showing that this scheme is of second order accuracy in space discretization. Applications of the method to other boundary conditions, including pressure condition and flux condition are discussed.

Two-layer approximate boundary conditions for large-eddy simulations

Abstract: A new method to model the effect of the solid boundaries on the rest of the flowfield in large-eddy simulations is proposed The filtered Navier-Stokes equations are solved up to the first computational point From there to the wall, a simplified set of equations is solved, and an estimate of the instantaneous wall shear stress required to impose boundary conditions is obtained Computations performed for the plane channel, square duct, and the rotating channel flow cases gave improved results compared with existing models The additional computing time required by the model is on the order of 10-15% of the overall computing time The mean flow quantities and low-order statistics, which are of primary interest in engineering calculations, are in very good agreement with the reference data available in the literature

Radiation and outflow boundary conditions for direct computation of acoustic and flow disturbances in a nonuniform mean flow

Abstract: It is well known that Euler equations support small amplitude acoustic, vorticity and entropy waves. To perform high quality direct numerical simulations of flow generated noise problems, acoustic radiation boundary conditions are required along inflow boundaries. Along boundaries where the mean flow leaves the computation domain, outflow boundary conditions are needed to allow the acoustic, vorticity and entropy disturbances to exit the computation domain without significant reflection. A set of radiation and outflow boundary conditions for problems with nonuniform mean flows are developed in this work. Flow generated acoustic disturbances are usually many orders of magnitude smaller than that of the mean flow. To capture weak acoustic waves by direct computation (without first separating out the mean flow), the intensity of numerical noise generated by the numerical algorithm and the radiation and outflow boundary conditions (and the computer) must be extremely low. It is demonstrated by a test problem ...

Electroseismic wave properties

Abstract: In a porous material saturated by a fluid electrolyte, mechanical and electromagnetic disturbances are coupled. The coupling is due to an excess of electrolyte ions that exist in a fluid layer near the grain surfaces within the material; i.e., the coupling is electrokinetic in nature. The governing equations controlling the coupled electromagnetic‐seismic (or ‘‘electroseismic’’) wave propagation are presented for a general anisotropic and heterogeneous porous material. Uniqueness is derived as well as the statements of energy conservation and reciprocity. Representation integrals for the various wave fields are derived that require, in general, nine different Green’s tensors. For the special case of an isotropic and homogeneous wholespace, both the plane‐wave and the point‐source responses are obtained. Finally, the boundary conditions that hold at interfaces in the porous material are derived.

A numerical free-surface condition for elastic/viscoelastic finite-difference modeling in the presence of topography

Abstract: An accurate free-surface boundary condition is important for solving a wide variety of seismic modeling problems. In particular, for earthquake site studies or shallow environmental investigations the surface of the earth may have a significant impact on the outcome of simulations. Computations based on several elastic/viscoelastic flat horizontal free-surface conditions are compared and benchmarked against an analytical solution. An accurate and simple condition is found and then generalized to allow for irregular free surfaces. This new method is simple to implement in conventional staggered finite-difference schemes, is computationally efficient and enables modeling of highly irregular topography. The accuracy of the method is investigated and criteria for sampling of the wavefield are derived.

Experimental verification of a modified scaling group for spontaneous imbibition

Abstract: Spontaneous imbibition is of critical importance to oil recovery from fractured reservoirs. A widely used approach to prediction of oil recovery involves scale-up of laboratory results to reservoir conditions. Scaling involves the effects of sample size, shape, boundary conditions, viscosity and viscosity ratios, interfacial tension, pore structure, wettability, capillary pressure and relative permeability. This work addresses the problem of scaling the combined effects of sample shape, boundary conditions, and viscosity ratios with only minor variations in other parameters. Imbibition measurements are presented for cylindrical Berea Sandstone cores of different lengths. For some experiments, core surfaces were partially sealed with epoxy to give different boundary conditions. Cores were initially saturated with refined mineral oils of different viscosities. A synthetic reservoir brine was used as the wetting phase. A characteristic length was defined as the square root of the ratio of volume to the summation of the ratios of area of core surface open to imbibition to the corresponding distance from the surface to the no-flow boundary. The characteristic length, in combination with a term that compensates for the effect of viscosity ratio, gave close correlation of all data.

Hyperbolic reductions for Einstein's equations

Abstract: We consider the problem of reducing initial value problems for Einstein's field equations to initial value problems for hyperbolic systems, a problem of importance for numerical as well as analytical investigations of gravitational fields. The main steps and the most important objectives in designing hyperbolic reductions are discussed. Various reductions which have already been studied in the literature or which can easily be derived from previous discussions of the field equations are pointed out and some of their specific features are indicated. We propose new reductions based on the use of the Bianchi equation for the conformal Weyl tensor. These reductions involve symmetric hyperbolic systems of propagation equations and allow a number of different gauge conditions. They use unknowns in a most economic way, supplying direct and non-redundant information about the geometry of the time slicing and the four-dimensional spacetime. Some of this information is directly related to concepts of gravitational radiation. All these reductions can be extended to include the conformal field equations. Those which are based on the ADM representation of the metric can be rewritten in flux conserving form.

A boundary element solution for a mode conversion study on the edge reflection of Lamb waves

Abstract: The boundary element method, well known for bulk wave scattering, is extended to study the mode conversion phenomena of Lamb waves from a free edge. The elastodynamic interior boundary value problem is formulated as a hybrid boundary integral equation in conjunction with the normal mode expansion technique based on the Lamb wave dispersion equation. The present approach has the potential of easily handling the geometrical complexity of general guided wave scattering with improved computational efficiency due to the advantage of the boundary‐type integral method. To check the accuracy of the boundary element program, vertical shear wave diffraction, due to a circular hole, is solved and compared with previous analytical solutions. Edge reflection factors for the multibackscattered modes in a steel plate are satisfied quite well with the principle of energy conservation. In the cases of A0, A1, and S0 incidence, the variations of the multireflection factors show similar tendencies to the existing results fo...

Cloud-Resolving Modeling of Tropical Cloud Systems during Phase III of GATE. Part I: Two-Dimensional Experiments.

Abstract: A formal framework is established for the way in which cloud-resolving numerical models are used to investigate the role of precipitating cloud systems in climate and weather forecasting models. Emphasis is on models with periodic lateral boundary conditions that eliminate unrealistic numerically generated circulations caused by open boundary conditions in long-term simulations. Defined in this formalism is the concept of large-scale forcing and the cloud-environment interactions that are consistent with the periodic boundary conditions. Two-dimensional numerical simulations of the evolution of cloud systems during 1–7 September 1974 in Phase III of the Global Atmospheric Research Program Atlantic Tropical Experiment (GATE) are conducted. Based on the above formalism, a simple technique is used to force an anelastic cloud-resolving model with evolving large-scale horizontal wind field and large-scale forcing for the temperature and moisture obtained from the GATE data. The 7-day period selected i...

A Particle Numerical Model for Wall Film Dynamics in Port-Injected Engines

Abstract: To help predict hydrocarbon emissions during cold-start conditions the authors are developing a numerical model for the dynamics and vaporization of the liquid wall films formed in port-injected spark-ignition engines and incorporating this model in the KIVA-3 code for complex geometries. This paper summarizes the current status of the project and presents illustrative example calculations. The dynamics of the wall film is influenced by interactions with the impinging spray, the wall, and the gas flow near the wall. The spray influences the film through mass, tangential momentum, and energy addition. The wall affects the film through the no-slip boundary condition and heat transfer. The gas alters film dynamics through tangential stresses and heat and mass transfer in the gas boundary layers above the films. New wall functions are given to predict transport in the boundary layers above the vaporizing films. It is assumed the films are sufficiently thin that film flow is laminar and that liquid inertial forces are negligible. Because liquid Prandtl numbers are typically about then, unsteady heating of the film should be important and is accounted for by the model. The thin film approximation breaks down near sharp corners, where an inertial separation criterion is used. A particle numerical method is used for the wall film. This has the advantages of compatibility with the KIVA-3 spray model and of very accurate calculation of convective transport of the film. The authors have incorporated the wall film model into KIVA-3, and the resulting combined model can be used to simulate the coupled port and cylinder flows in modern spark-ignition engines. They give examples by comparing computed fuel distributions with closed- and open-valve injection during the intake and compression strokes of a generic two-valve engine.

Heat kernel coefficients of the Laplace operator on the D‐dimensional ball

Abstract: We present a very quick and powerful method for the calculation of heat kernel coefficients. It makes use of rather common ideas, as integral representations of the spectral sum, Mellin transforms, non‐trivial commutation of series and integrals and skillful analytic continuation of zeta functions on the complex plane. We apply our method to the case of the heat kernel expansion of the Laplace operator on a D‐dimensional ball with either Dirichlet, Neumann or, in general, Robin boundary conditions. The final formulas are quite simple. Using this case as an example, we illustrate in detail our scheme —which serves for the calculation of an (in principle) arbitrary number of heat kernel coefficients in any situation when the basis functions are known. We provide a complete list of new results for the coefficients B3,..., B10, corresponding to the D‐dimensional ball with all the mentioned boundary conditions and D=3,4,5.

On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions

Abstract: For boundary or distributed controls, we get an approximate controllability result for the Navier-Stokes equations in dimension 2 in the case where the fluid is incompressible and slips on the boundary in agreement with the Navier slip boundary conditions.