Computational simulation of chemical dissolution‐front instability in fluid‐saturated porous media under non‐isothermal conditions

This paper primarily deals with the computational aspects of chemical dissolution‐front instability problems in two‐dimensional fluid‐saturated porous media under non‐isothermal conditions. After the dimensionless governing partial differential equations of the non‐isothermal chemical dissolution‐front instability problem are briefly described, the formulation of a computational procedure, which contains a combination of using the finite difference and finite element method, is derived for simulating the morphological evolution of chemical dissolution fronts in the non‐isothermal chemical dissolution system within two‐dimensional fluid‐saturated porous media. To ensure the correctness and accuracy of the numerical solutions, the proposed computational procedure is verified through comparing the numerical solutions with the analytical solutions for a benchmark problem. As an application example, the verified computational procedure is then used to simulate the morphological evolution of chemical dissolution fronts in the supercritical non‐isothermal chemical dissolution system. The related numerical results have demonstrated the following: (1) the proposed computational procedure can produce accurate numerical solutions for the planar chemical dissolution‐front propagation problem in the non‐isothermal chemical dissolution system consisting of a fluid‐saturated porous medium; (2) the Zhao number has a significant effect not only on the dimensionless propagation speed of the chemical dissolution front but also on the distribution patterns of the dimensionless temperature, dimensionless pore‐fluid pressure, and dimensionless chemical‐species concentration in a non‐isothermal chemical dissolution system; (3) once the finger penetrates the whole computational domain, the dimensionless pore‐fluid pressure decreases drastically in the non‐isothermal chemical dissolution system.     

Numerical modelling of chemical effects of magma solidification problems in porous rocks

The solidification of intruded magma in porous rocks can result in the following two consequences: (1) the heat release due to the solidification of the interface between the rock and intruded magma and (2) the mass release of the volatile fluids in the region where the intruded magma is solidified into the rock. Traditionally, the intruded magma solidification problem is treated as a moving interface (i.e. the solidification interface between the rock and intruded magma) problem to consider these consequences in conventional numerical methods. This paper presents an alternative new approach to simulate thermal and chemical consequences/effects of magma intrusion in geological systems, which are composed of porous rocks. In the proposed new approach and algorithm, the original magma solidification problem with a moving boundary between the rock and intruded magma is transformed into a new problem without the moving boundary but with the proposed mass source and physically equivalent heat source. The major advantage in using the proposed equivalent algorithm is that a fixed mesh of finite elements with a variable integration time‐step can be employed to simulate the consequences and effects of the intruded magma solidification using the conventional finite element method. The correctness and usefulness of the proposed equivalent algorithm have been demonstrated by a benchmark magma solidification problem. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical solution of the heat equation with non‐linear,time derivative‐dependent source term

The mathematical modeling of heat conduction with adsorption effects in coated metal structures yields the heat equation with piecewise smooth coefficients and a new kind of source term. This term is special, because it is non‐linear and furthermore depends on a time derivative. In our approach we reformulated this as a new problem for the usual heat equation, without source term but with a new non‐linear coefficient. We gave an existence and uniqueness proof for the weak solution of the reformulated problem. To obtain a numerical solution, we developed a semi‐implicit and a fully implicit finite volume method. We compared these two methods theoretically as well as numerically. Finally, as practical application, we simulated the heat conduction in coated aluminum fibers with adsorption in the zeolite coating. Copyright © 2010 John Wiley & Sons, Ltd.     

Redemption of the formalism of segmented linearity: multiscaling of non‐equilibrium and non‐homogeneity applied to fatigue crack growth

At the risk of being presumptuous, the influence of non‐equilibrium and non‐homogeneity (NENH) is the key to explain the conundrums of today's physics and mechanics on the basis of the NENH Mechanics of Multiscaling (NNMM). Corrective measures have been used to correct errors caused by the neglect of NENH and multiscaling. The separate conservation of mass and energy is a case in point. The inclusion of NENH leads to the simultaneous conservation of mass and energy as a product. The revised conservation law depends on the degree of system inhomogeneity. The aforementioned vouches the credibility for applying NNMM to resolve the impasse of the misinterpreted fatigue crack growth (FCG) data using monoscale concepts. The new paradigm is fundamental to contrast the difference between deterministic and non‐deterministic. The phenomena of turbulence and instability in general are determinable when the thresholds are related to the appropriate physical mechanism at the temporal–spatial scale. The correct experiments depend on identifying the role with which NNMM plays in the physical phenomenon. The same applies to FCG. To reiterate, the aim is not to develop new theories but rather to offer corrective measures by including NENH and multiscaling to show that the understanding of FCG is no less challenging than some of the conundrums of physics and mechanics of today.     

An algorithm and a method to search bifurcation points in non‐linear problems

This paper is devoted to a numerical method able to help the determination of the bifurcation threshold in non‐linear time‐independent continuum mechanic problems. First, some theoretical results about uniqueness are recalled. In the framework of the large‐strain assumption, the differences between the classical finite‐step problem and the rate problem are presented. An iterative algorithm able to solve the rate problem is given. Using different initializations, it is seen in some numerical experiments that it is possible with this algorithm to get different solutions when the underlying mathematical problem solved does not enjoy a uniqueness property. The constitutive equations used have been chosen to be simple enough to deduce some theoretical knowledge about the corresponding uniqueness problems. Finally, a method is given which is able in some case to give an upper bound of the bifurcation threshold. Copyright © 2001 John Wiley & Sons, Ltd.     

QALE‐FEM for numerical modelling of non‐linear interaction between 3D moored floating bodies and steep waves

This paper presents further development of the quasi arbitrary Lagrangian–Eulerian finite element method (QALE‐FEM) based on a fully non‐linear potential theory to numerically simulate non‐linear responses of 3D moored floating bodies to steep waves. In the QALE‐FEM (recently developed by the authors and applied to 2D floating bodies), the complex unstructured mesh is generated only once at the beginning of calculation and is moved to conform to the motion of boundaries at other time steps by using a robust spring analogy method specially suggested for these kind of problems, avoiding the necessity of high‐cost remeshing. In order to tackle challenges associated with 3D floating bodies, several new numerical techniques are developed in this paper. These include the technique for moving the mesh near body surfaces, the scheme for calculating velocity on 3D body surfaces and the modified semi‐implicit time integration method for floating bodies procedure (ISITIMFB‐M) that is more efficient for dealing with the full coupling between waves and bodies. Using the newly developed techniques and methods, various cases for 3D floating bodies with motions of up to six degrees of freedom (DoFs) are simulated. These include a SPAR platform, a barge‐type floating body and one or two Wigley Hulls in head seas or in oblique waves. For some selected cases, the numerical results are compared with experimental data available in the public domain and satisfactory agreements are achieved. Many results presented in this paper have not been found elsewhere to the best knowledge of the authors. Copyright © 2008 John Wiley & Sons, Ltd.     

An integrated,finite element‐based process model for the analysis of flow,heat transfer,and solidification in a continuous slab caster

An integrated, finite element‐based process model is presented for the prediction of full three‐dimensional flow, heat transfer, and solidification occurring in a continuous caster. Described in detail are the basic models for the analysis of turbulent flow and heat transfer in the liquid steel zone, in the zone of mixture of the liquid steel and solidified steel, and in the solidified zone. Then, the models are integrated to form a process model which can take into account the strong interdependence between the heat transfer behaviour and the flow behaviour. The capability of the process model to reveal the detailed aspects of turbulent flow, heat transfer, and solidification occurring in a continuous caster is demonstrated through a series of process simulations. Copyright © 2003 John Wiley & Sons, Ltd.