OPERATOR-SPLITTING GALERKIN METHOD FOR ONE KIND OF OIN REACTION MODEL FOR THE POLLUTION IN GROUNDWATER

The operator-splitting methods for the mathematic model of one kind of oin reactions for the problem of groundwater are considered.Optimal error estimates in L 2 and H 1 norm are obtained for the approximation solution.

THE MODIFIED METHOD OF CHARACTERISTICS WITH FINITE ELEMENT OPERATOR-SPLITTING PROCEDURES FOR COMPRESSIBLE MULTICOMPONENT DISPLACEMENT PROBLEM

For the three-dimensional compressible multicomponent displacement problem we put forward the modified method of characteristics with finite element operator-splitting procedures and make use of operator-splitting,characteristic method,calculus of variations,energy method,negative norm estimate,two kinds of test functions and the theory of prior estimates and techniques.Optimal order estimates in L^2 norm are derived for the error in the approximate solution.These methods have been successfully used in oil-gas resources estimation,enhanced oil recovery simulation and seawater intrusion numerical simulation.

AN OPERATOR-SPLITTING ALGORITHM FOR THREE-DIMEN-SIONAL CONVECTION-DIFFUSION PROBLEMS

An operator-splitting algorithm for the three-dimensional convection-diffusion equa- tion is presented.The flow region is discretized into tetrahedronal elements which are fixed in time. The transport equation is split into two successive initial value problems:a pure convection problem and a pure diffusion problem.For the pure convection problem,solutions are found by the method of characteristiCS.The solution algorithm involves tracing the characteristic lines backwards in time from a vertex of an element to an interior point.A cubic polynomial is used to interpolate the concentration and its derivatives within each element.For the diffusion problem,an explicit finite element algorithm is employed.Numerical examples are given which agree well with the analytical solutions.

OPERATOR-SPLITTING METHOD FOR ANALYSIS OF CAVITATION IN LIQUID-LUBRICATED HERRINGBONE GROOVED JOURNAL BEARING

This paper presents an Operator -Splitting Method (OSM) for the solution of the universal Reynolds equation. Jakoobsson-Floberg-Olsson (JFO) pressure conditions were incorporated for the study of cavitation in a liquid-lubricated journal bearings. Shear flow component of the oil film was first solved by a modified upwind finite difference method. The solution of the pressure gradient flow component was completed by the Galerkin finite element method. Present OSM solutions for a slider bearing are in agreement with Elord's results. OSM was then applied to herringbone grooved journal bearing in this work. The film pressure, cavitation areas, load capacity and attitude angle were obtained with JFO pressure conditions. The calculated load capacities are in agreement with Hirs's experimental data. A comparison of the present results and those predicted by the Reynolds pressure conditions shows some differences. The numerical results indicate that the load capacity and the critical mass of journal (linear stability indicator) are higher, and the attitude angle is lower than those predicted by Reynolds pressure conditions in cases of high eccentricities.

Fourth-Order Splitting Methods for Time-Dependant Differential Equations

This study was suggested by previous work on the simulation of evolution equations with scale-dependent processes,e.g.,wave-propagation or heat-transfer,that are modeled by wave equations or heat equations.Here,we study both parabolic and hyperbolic equations.We focus on ADI (alternating direction implicit) methods and LOD (locally one-dimensional) methods,which are standard splitting methods of lower order,e.g.second-order.Our aim is to develop higher-order ADI methods,which are performed by Richardson extrapolation,Crank-Nicolson methods and higher-order LOD methods,based on locally higher-order methods.We discuss the new theoretical results of the stability and consistency of the ADI methods.The main idea is to apply a higher- order time discretization and combine it with the ADI methods.We also discuss the dis- cretization and splitting methods for first-order and second-order evolution equations. The stability analysis is given for the ADI method for first-order time derivatives and for the LOD (locally one-dimensional) methods for second-order time derivatives.The higher-order methods are unconditionally stable.Some numerical experiments verify our results.

Simulating the dynamics of fluid-cylinder interactions

We present the simulation of the dynamics of fluid-cylinder interactions in a narrow three-dimensional channel filled with a Newtonian fluid, using a Lagrange multiplier based fictitious domain methodology combined with a finite element method and an operator splitting technique. As expected, a settling truncated cylinder turns its broadside perpendicular to the main stream direction and the center of mass moves to the central axis of the channel. In the case of two truncated cylinders, they first move around each other for a while and then stay together in a "T" shape. After the "T" shape has been formed for a long enough time, we found no vortex shedding behind the cylinders. When simulating the fluidization of 60 truncated cylinders, we captured the features of interactions among fluidized cylinders as observed in experiments.

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This article discusses computational methods for the numerical simulation of unsteady Bingham visco-plastic flow. These methods are based on time-discretization by operator-splitting and take advantage of a characterization of the solutions involving some kind of Lagrange multipliers. The full discretization is achieved by combining the above operator-splitting methods with finite element approximations, the advection being treated by a wave-like equation 'equivalent' formulation easier to implement than the method of characteristics or high order upwinding methods. The authors illustrate the methodology discussed in this article with the results of numerical experiments concerning the simulation of wall driven cavity Bingham flow in two dimensions.

Online hybrid test using a finite element program and an explicit integration scheme

A new online hybrid test system combined with substructuring techniques and incorporating finite element methods is developed.In the proposed system,numerical substructure analysis is conducted by ABAQUS/Explicit.An ABAQUS user subroutine is used as the interface between the main control program and ABAQUS to impose the target displacements and determine the reaction forces.No iteration is needed in this system,making it suitable for physical testing.As the approach also avoids the need to modify source code,it will be appealing to a number of real engineering applications.The proposed system adopts a separated-model framework,operator-splitting integration scheme,and data exchange through a socket mechanism.The earthquake responses of a simple steel moment-resisting frame are simulated,and the results obtained from the new system are compared to those obtained from the conventional analysis.It is found that the results obtained from the new system are accurate,demonstrating the applicability and efficiency of the proposed approach.The optimal test parameters are also studied to gain the most accurate results in the minimum time.

CHARACTERISTIC ALTERNATING-DIRECTION FINITE ELEMENT METHODS FOR NONRECTANGULAR REGIONS FOR COUPLED SYSTEM OF DYNAMICS OF FLUIDS IN POROUS MEDIA AND ITS ANALYSIS

For coupled system of multilayer dynamics of fluids in porous media, thecharacteristic alternating-direction finite element methods for nonrectangular regions applicable toparallel arithmetic are put forward and two-dimensional and three-dimensional schemes are used toform a complete set. Some techniques, such as calculus of variations, isoparametric transformation,patch approximation, operator-splitting, characteristic method, negative norm estimate, energymethod, the theory of prior estimates and techniques are used. For the nonrectangular regions case,optimal order estimates in L^2 norm are derived for the error in the approximation solution. Thusthe well-known theoretical problem has been thoroughly and completely solved. These methods havebeen successfully used in multilayer oil resources migration-accumulation numerical simulation.

NUMERICAL MODELING AND OPTIMAL ESTIMATION OF THE TRANSPORT OF GROUNDWATER POLLUTION

A numerical method for coupled solution of the equations of groundwater flow and pollution transportation is presented on the basis of operator-splitting algorithm, and the application of Kalman filtering technique into the study of groundwater pollution are explored also in the present paper. Computative examples indicate that the numerical method and application of Kalman theory can avoid the unhealthy tendencies in numerical modeling and hence attain the computative accuracy considerably.

Efficient three-dimensional high-resolution simulations of flow fields around cylinders

Few works use the fully three-dimensional computational fluid dynamic method to simulate the flow fields around the marine pipes with large aspect ratios due to the huge computation cost.In the present work,an operator-splitting method is used to efficiently solve the three-dimensional Reynolds Average Navier-Stokes governing equations of the fluid flow around pipes by separating the problem as a combination of a two-dimensional problem in the horizontal plane and an one-dimensional problem in the vertical direction.A second order total variation diminishing finite volume method is used to solve the model.The precision of the present model is validated by comparing the present numerical results of two typical three-dimensional cases with the available experimental and numerical results.The simulation results with a commercial software are also included in the comparison and the present model shows a higher performance in terms of computational time.