A fast explicit finite difference method for determination of wellhead injection pressure

A fast explicit finite difference method (FEFDM),derived from the differential equations of one-dimensional steady pipe flow,was presented for calculation of wellhead injection pressure.Recalculation with a traditional numerical method of the same equations corroborates well the reliability and rate of FEFDM.Moreover,a flow rate estimate method was developed for the project whose injection rate has not been clearly determined.A wellhead pressure regime determined by this method was successfully applied to the trial injection operations in Shihezi formation of Shenhua CCS Project,which is a good practice verification of FEFDM.At last,this method was used to evaluate the effect of friction and acceleration terms on the flow equation on the wellhead pressure.The result shows that for deep wellbore,the friction term can be omitted when flow rate is low and in a wide range of velocity the acceleration term can always be deleted.It is also shown that with flow rate increasing,the friction term can no longer be neglected.

Unified elastoplastic finite difference and its application

Two elastoplastic constitutive models based on the unified strength the- ory （UST） are established and implemented in an explicit finite difference code, fast Lagrangian analysis of continua （FLAC/FLAC3D）, which includes an associated/non- associated flow rule, strain-hardening/softening, and solutions of singularities. Those two constitutive models are appropriate for metallic and strength-different （SD） materials, respectively. Two verification examples are used to compare the computation results and test data using the two-dimensional finite difference code FLAC and the finite element code ANSYS, and the two constitutive models proposed in this paper are verified. Two application examples, the large deformation of a prismatic bar and the strain-softening be- havior of soft rock under a complex stress state, are analyzed using the three-dimensional code FLAC3D. The two new elastoplastic constitutive models proposed in this paper can be used in bearing capacity evaluation or stability analysis of structures built of metallic or SD materials. The effect of the intermediate principal stress on metallic or SD mate- rial structures under complex stress states, including large deformation, three-dimensional and non-association problems, can be analyzed easily using the two constitutive models proposed in this paper.

Hall Effect on ECF Flow along a Rotating Infinite Porous Plate in the Presence of Transverse Magnetic Field

Unsteady extracellular fluid (ECF) flow along with a rotating infinite vertical porous plate in the presence of a transverse magnetic field has been studied numerically. The dimensional governing equations have been non-dimensionalized by useful dimensionless variables. The explicit finite difference method has been used to solve dimensionless equations. The numerical results have been calculated by studio developer FORTRAN 6.6a and MATLAB 2018a. For perfect conducting case, Magnetic Diffusivity Parameter 5 ≤ Pm ≤ 15 has been taken in induction equation. For good accuracy, stability and convergence analysis have been analyzed. Mesh Sensitivity test, steady-state solution test, and code validation test have been performed. For time step τ = 1, the numerical results have been found for the primary velocity, secondary velocity, angular velocity, primary induced magnetic field, secondary induced magnetic field, temperature as well as shear stresses along x and z direction, couple stress along z direction, current densities along x and z direction and the Nusselt number. Finally, the effects of various parameters have been separately discussed and illustrated graphically.

AN EXPLICIT MULTI-CONSERVATION FINITE-DIFFERENCE SCHEME FOR SHALLOW-WATER-WAVE EQUATION

An explicit multi-conservation finite-difference scheme for solving the spherical shallow-water-wave equation set of barotropic atmosphere has been proposed. The numerical scheme is based on a special semi-discrete form of the equations that conserves four basic physical integrals including the total energy, total mass, total potential vorticity and total enstrophy. Numerical tests show that the new scheme performs closely like but is much more time-saving than the implicit multi-conservation scheme.

A Study of Two Dimensional Unsteady MHD Free Convection Flow over a Vertical Plate

In this paper, unsteady free convection heat transfer flow over a vertical plate in the presence of a magnetic field is discussed in detail. The dimensionless partial differential equations of continuity, momentum along energy are analyzed with suitable transformations. For numerical calculation, an implicit finite difference method is applied to solve a set of nonlinear dimensionless partial differential equations. Dimensionless velocity and temperature profile are also investigated due to the effects of assumed parameters in the concerned problem. An explicit finite difference technique is used to compute velocity and temperature profiles. The stability conditions are also examined.

Unsteady Electromagnetic Free Convection Micropolar Fluid Flow through a Porous Medium along a Vertical Porous Plate

Unsteady electromagnetic free convection flows of two-dimensional micropolar fluid through in a porous medium parallel to a vertical porous plate have been investigated numerically. Similarity analysis has been used to transform the governing equations into its non-dimensional form by using the explicit finite difference method to obtain numerical solutions. Estimated results have been gained for various values of Prandtl number, Grashof number, material parameters, micropolar parameter, electric conductivity, electric permeability, thermal relaxation time and the permeability of the porous medium. The effects of pertinent parameters on the velocity, electric induction, magnetic induction, microrotation and temperature distributions have been investigated briefly and illustrated graphically.

Impulsively Started Horizontal Riga Plate Embedded in Unsteady Casson Fluid Flow with Rotation

This article is based on the impulsively started horizontal Riga plate in two dimensional unsteady Casson fluid flows with rotation. The plate starts abruptly from the rest relative to the rotating fluids moving with uniform acceleration in its plane. Numerical solutions are acquired by using explicit finite difference method and estimated results have been gained for various values of the Rotational parameter, modified Hartmann number, Prandtl number, Radiative parameter, Eckert number, Heat source parameter, Schmidt number, and the Soret number. Both the Compaq visual FORTRAN 6.6a and MATLAB R2015a tools have been used to find the numerical solutions and the graphical presentation. The Skin friction, Nusselt number and Sherwood number have been computed and the effects of some pertinent parameters on various distributions are discussed briefly and presented graphically.

The Effect Analysis of Topography on the Spectrum Properties of Anti-Plane Movement

An explicit finite difference method is performed to evaluate the significance of topography effects on the seismic response of viscoelastic sites.The real accelerograms and bell-shape impulse wavelets,slope angle of cliff and angle of incidence on the spectrum property of the incoming waves are all discussed in detail.The conclusions show that the presence of topographic factors and the direction of the incident waves not only significantly affect the peak ground acceleration of a site,but also affect the spectrum properties of the incoming waves,and the effect on the direction of the incident waves is especially remarkable.The study also finds that it is reasonable to analyse spectrum properties with the input of impulse wavelets in the finite element simulation of wave motion.