scholarly journals Durability of Subsea Tunnels under the Coupled Action of Stress and Chloride Ions

2019 ◽  
Vol 9 (10) ◽  
pp. 1984
Author(s):  
Qingli Zhao ◽  
Limin Lu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Service Life ◽  
Reliability Index ◽  
Chloride Ion ◽  
Chloride Ions ◽  
Ion Concentration ◽  
Influence Coefficient ◽  
Partial Differential ◽  
Convection Diffusion

The durability of subsea tunnels under the coupled action of stress and chloride ions was analyzed to estimate the service life and provide a theoretical foundation for durability design. The influence coefficient of the stress on chloride ion transmission at lower stress levels was discussed according to the material mechanics, and was verified by experimental data. A stress calculation model of a subsea tunnel’s lining section is proposed based on the plane-section assumption. Considering the space-time effect of the convection velocity, a partial differential equation was constructed to calculate the chloride ion transfer condition under the coupled action of stress-convection-diffusion. The numerical solution of the partial differential equation was solved and the sensitivity of the parameters was analyzed. The subsea tunnel’s time-varying reliability index was calculated following the Monte Carlo method, and was used to predict the service life. The results show that the chloride ion concentration calculated by considering the coupled action is larger and the reliability index is lower than calculated only considering diffusion. Our findings contribute to the conclusion that durability designs of subsea tunnels should consider the coupled action of stress-convection-diffusion. An effective method to improve the service life of a subsea tunnel is to reduce the water–binder ratio or increase the thickness of protective cover.

scholarly journals Higher-Order Linear-Time Unconditionally Stable Alternating Direction Implicit Methods for Nonlinear Convection-Diffusion Partial Differential Equation Systems

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Oscar P. Bruno ◽  
Edwin Jimenez
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Linear Time ◽  
High Order Accuracy ◽  
Implicit Methods ◽  
Partial Differential ◽  
Nonlinear Convection ◽  
Alternating Direction Implicit ◽  
Convection Diffusion ◽  
Alternating Direction

We introduce a class of alternating direction implicit (ADI) methods, based on approximate factorizations of backward differentiation formulas (BDFs) of order p≥2, for the numerical solution of two-dimensional, time-dependent, nonlinear, convection-diffusion partial differential equation (PDE) systems in Cartesian domains. The proposed algorithms, which do not require the solution of nonlinear systems, additionally produce solutions of spectral accuracy in space through the use of Chebyshev approximations. In particular, these methods give rise to minimal artificial dispersion and diffusion and they therefore enable use of relatively coarse discretizations to meet a prescribed error tolerance for a given problem. A variety of numerical results presented in this text demonstrate high-order accuracy and, for the particular cases of p=2,3, unconditional stability.

scholarly journals On the numerical solution of the one-dimensional convection-diffusion equation

2005 ◽  
Vol 2005 (1) ◽  
pp. 61-74 ◽  
Author(s):  
Mehdi Dehghan
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Diffusion Equation ◽  
Numerical Solution ◽  
Partial Differential ◽  
One Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
The One

The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flow, in the modeling of semiconductors, and so forth. This paper describes several finite difference schemes for solving the one-dimensional convection-diffusion equation with constant coefficients. In this research the use of modified equivalent partial differential equation (MEPDE) as a means of estimating the order of accuracy of a given finite difference technique is emphasized. This approach can unify the deduction of arbitrary techniques for the numerical solution of convection-diffusion equation. It is also used to develop new methods of high accuracy. This approach allows simple comparison of the errors associated with the partial differential equation. Various difference approximations are derived for the one-dimensional constant coefficient convection-diffusion equation. The results of a numerical experiment are provided, to verify the efficiency of the designed new algorithms. The paper ends with a concluding remark.

Optimal Identification of Parameters in an Inhomogeneous Medium With Quadratic Programming

1975 ◽  
Vol 15 (05) ◽  
pp. 371-375 ◽  
Author(s):  
W.W-G. Yeh
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Linear Programming ◽  
Parameter Identification ◽  
Governing Equation ◽  
Space Variable ◽  
Computer Time ◽  
Influence Coefficient ◽  
Partial Differential ◽  
Aquifer System

Abstract The paper develops a new algorithm for parameter identification in a partial differential equation associated with an inhomogeneous aquifer system. The parameters chosen for identification are the storage coefficient, a constant, and transmissivities, functions of the space variable. An implicit finite-difference scheme is used to approximate the solutions of the governing equation. A least-squares criterion is then established. Using distributed observations on the dependent variable within the system, parameters are identified directly by solving a sequence of quadratic programming problems such that the final solution converges to the original problem. The advantages of this new algorithm problem. The advantages of this new algorithm include rapid rate of convergence, ability to handle any inequality constraints, and easy computer implementation. The numerical example presented demonstrates the simultaneous identification of 12 parameters in only seconds of computer time. parameters in only seconds of computer time Introduction Simulation and mathematical models are often used in analyzing aquifer systems. Physically based mathematical models are implemented by high-speed computers. Most models are of a parametric type, in which parameters used in parametric type, in which parameters used in deriving the governing equation are not measurable directly from the physical point of view and, therefore, must be determined from historical records. The literature dealing with parameter identification in partial differential equations has become available only within the last decade. The approaches include gradient searching procedures, the balanced error-weighted gradient method, the classical Gauss-Newton least-squares procedure, optimal control and gradient optimization, quasi linearization, influence coefficient algorithm, linear programming, maximum principle, and regression analysis allied with the steepest-descent algorithm. Yeh analyzed a typical parameter identification problem governed by a second-order, nonlinear, parabolic partial differential equation using five different methods (the gradient method, quasilinearization, maximum principle, influence coefficient method, and linear programming) and then compared these methods. The problem under consideration is that of an unsteady radial flow in a confined aquifer system. The governing equation is(1)1 h h--- --- rT(r) ----- = S ------ + Q, r r r t subject to the following initial and boundary conditions:0t = 0, h = h, 0 < r < re(2)r= 0, h = h (t), t >00Bhr = r ----- = 0, t >0e r Eq. 1 represents a distributed system in which parameters are functions of the space variable. The parameters are functions of the space variable. The assumptions used in deriving Eq. 1 include (1) the aquifer is confined with a constant depth, b; (2) the aquifer overlays on an infinite horizontal impermeable bed; (3) the Dupuit-Forchheimer assumptions are valid; and (4) water is released instantaneously because of the change of the flow potential. SPEJ P. 371

Qxygen transfer in gravity flow sewers

2000 ◽  
Vol 42 (3-4) ◽  
pp. 417-422 ◽  
Author(s):  
T.Y. Pai ◽  
C.F. Ouyang ◽  
Y.C. Liao ◽  
H.G. Leu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dissolved Oxygen ◽  
Flow Velocity ◽  
Molecular Diffusion ◽  
Eddy Diffusion ◽  
Partial Differential ◽  
Diffusion Term ◽  
Sewer Pipes ◽  
Gravity Sewer

Oxygen diffused to water in gravity sewer pipes was studied in a 21 m long, 0.15 m diameter model sewer. At first, the sodium sulfide was added into the clean water to deoxygenate, then the pump was started to recirculate the water and the deoxygenated water was reaerated. The dissolved oxygen microelectrode was installed to measure the dissolved oxygen concentrations varied with flow velocity, time and depth. The dissolved oxygen concentration profiles were constructed and observed. The partial differential equation diffusion model that considered Fick's law including the molecular diffusion term and eddy diffusion term were derived. The analytic solution of the partial differential equation was used to determine the diffusivities by the method of nonlinear regression. The diffusivity values for the oxygen transfer was found to be a function of molecular diffusion, eddy diffusion and flow velocity.

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