Theory manual to OctVCE – a cartesian cell CFD code with special application to blast wave problems, Department of Mechanical Engineering Report 2007/12

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries, in particular, from explosions. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel for its simplicity and sufficiency for practical engineering design problems. The code uses a finite-volume formulation of the unsteady Euler equations with a second order explicit Runge-Kutta Godonov (MUSCL) scheme. Gradients are calculated using a least-squares method with a minmod limiter. Flux solvers used are AUSM, AUSMDV and EFM. No fluid-structure coupling or chemical reactions are allowed, but gas models can be perfect gas and JWL or JWLB for the explosive products. This report also describes the code’s ‘octree’ mesh adaptive capability and point-inclusion query procedures for the VCE geometry engine. Finally, some space will also be devoted to describing code parallelization using the shared-memory OpenMP paradigm. The user manual to the code is to be found in the companion report 2007/13.

User guide for shock and blast simulation with the OctVCE code (version 3.5+), Department of Mechanical Engineering Report 2007/13

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel as it is simple to code and sufficient for practical engineering design problems. This also makes the code much more ‘user-friendly’ than structured grid approaches as the gridding process is done automatically. The CFD methodology relies on a finite-volume formulation of the unsteady Euler equations and is solved using a standard explicit Godonov (MUSCL) scheme. Both octree-based adaptive mesh refinement and shared-memory parallel processing capability have also been incorporated. For further details on the theory behind the code, see the companion report 2007/12.

Effects of geological inhomogeneity on high Rayleigh number steady state heat and mass transfer in fluid-saturated porous media heated from below

A parametric study is carried out to investigate how geological inhomogeneity affects the pore-fluid convective flow field, the temperature distribution, and the mass concentration distribution in a fluid-saturated porous medium. The related numerical results have demonstrated that (1) the effects of both medium permeability inhomogeneity and medium thermal conductivity inhomogeneity are significant on the pore-fluid convective flow and the species concentration distribution in the porous medium; (2) the effect of medium thermal conductivity inhomogeneity is dramatic on the temperature distribution in the porous medium, but the effect of medium permeability inhomogeneity on the temperature distribution may be considerable, depending on the Rayleigh number involved in the analysis; (3) if the coupling effect between pore-fluid flow and mass transport is weak, the effect of the Lewis number is negligible on the pore-fluid convective flow and temperature distribution, hut it is significant on the species concentration distribution in the medium.

Modeling ex vivo hematopoiesis using chemical engineering metaphors

Ex vivo hematopoiesis is increasingly used for clinical applications. Models of ex vivo hematopoiesis are required to better understand the complex dynamics and to optimize hematopoietic culture processes. A general mathematical modeling framework is developed which uses traditional chemical engineering metaphors to describe the complex hematopoietic dynamics. Tanks and tubular reactors are used to describe the (pseudo-) stochastic and deterministic elements of hematopoiesis, respectively. Cells at any point in the differentiation process can belong to either an immobilized, inert phase (quiescent cells) or a mobile, active phase (cycling cells). The model describes five processes: (1) flow (differentiation), (2) autocatalytic formation (growth),(3) degradation (death), (4) phase transition from immobilized to mobile phase (quiescent to cycling transition), and (5) phase transition from mobile to immobilized phase (cycling to quiescent transition). The modeling framework is illustrated with an example concerning the effect of TGF-beta 1 on erythropoiesis. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.

Finite element analysis of flow patterns near geological lenses in hydrodynamic and hydrothermal systems

We use theoretical and numerical methods to investigate the general pore-fluid flow patterns near geological lenses in hydrodynamic and hydrothermal systems respectively. Analytical solutions have been rigorously derived for the pore-fluid velocity, stream function and excess pore-fluid pressure near a circular lens in a hydrodynamic system. These analytical solutions provide not only a better understanding of the physics behind the problem, but also a valuable benchmark solution for validating any numerical method. Since a geological lens is surrounded by a medium of large extent in nature and the finite element method is efficient at modelling only media of finite size, the determination of the size of the computational domain of a finite element model, which is often overlooked by numerical analysts, is very important in order to ensure both the efficiency of the method and the accuracy of the numerical solution obtained. To highlight this issue, we use the derived analytical solutions to deduce a rigorous mathematical formula for designing the computational domain size of a finite element model. The proposed mathematical formula has indicated that, no matter how fine the mesh or how high the order of elements, the desired accuracy of a finite element solution for pore-fluid flow near a geological lens cannot be achieved unless the size of the finite element model is determined appropriately. Once the finite element computational model has been appropriately designed and validated in a hydrodynamic system, it is used to examine general pore-fluid flow patterns near geological lenses in hydrothermal systems. Some interesting conclusions on the behaviour of geological lenses in hydrodynamic and hydrothermal systems have been reached through the analytical and numerical analyses carried out in this paper.

Numerical and experimental study of seepage in unconfined aquifers with a periodic boundary condition

The assessment of groundwater conditions within an unconfined aquifer with a periodic boundary condition is of interest in many hydrological and environmental problems. A two-dimensional numerical model for density dependent variably saturated groundwater flow, SUTRA (Voss, C.I., 1984. SUTRA: a finite element simulation model for saturated-unsaturated, fluid-density dependent ground-water flow with energy transport or chemically reactive single species solute transport. US Geological Survey, National Center, Reston, VA) is modified in order to be able to simulate the groundwater flow in unconfined aquifers affected by a periodic boundary condition. The basic flow equation is changed from pressure-form to mixed-form. The model is also adjusted to handle a seepage-face boundary condition. Experiments are conducted to provide data for the groundwater response to the periodic boundary condition for aquifers with both vertical and sloping faces. The performance of the numerical model is assessed using those data. The results of pressure- and mixed-form approximations are compared and the improvement achieved through the mixed-form of the equation is demonstrated. The ability of the numerical model to simulate the water table and seepage-face is tested by modelling some published experimental data. Finally the numerical model is successfully verified against present experimental results to confirm its ability to simulate complex boundary conditions like the periodic head and the seepage-face boundary condition on the sloping face. (C) 1999 Elsevier Science B.V. All rights reserved.

An equivalent algorithm for simulating thermal effects of magma intrusion problems in porous rocks

An equivalent algorithm is proposed to simulate thermal effects of the magma intrusion in geological systems, which are composed of porous rocks. Based on the physical and mathematical equivalence, 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 a physically equivalent heat source. From the analysis of an ideal solidification model, the physically equivalent heat source has been determined in this paper. The major advantage in using the proposed equivalent algorithm is that the fixed finite element mesh with a variable integration time step can be employed to simulate the thermal effect of the intruded magma solidification using the conventional finite element method. The related numerical results have demonstrated the correctness and usefulness of the proposed equivalent algorithm for simulating the thermal effect of the intruded magma solidification in geological systems. (C) 2003 Elsevier B.V. All rights reserved.

Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined.

Double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the double diffusion-driven convective instability of three-dimensional fluid-saturated geological fault zones when they are heated uniformly from below. The fault zone is assumed to be more permeable than its surrounding rocks. In particular, we have derived exact analytical solutions to the total critical Rayleigh numbers of the double diffusion-driven convective flow. Using the corresponding total critical Rayleigh numbers, the double diffusion-driven convective instability of a fluid-saturated three-dimensional geological fault zone system has been investigated. The related theoretical analysis demonstrates that: (1) The relative higher concentration of the chemical species at the top of the three-dimensional geological fault zone system can destabilize the convective flow of the system, while the relative lower concentration of the chemical species at the top of the three-dimensional geological fault zone system can stabilize the convective flow of the system. (2) The double diffusion-driven convective flow modes of the three-dimensional geological fault zone system are very close each other and therefore, the system may have the similar chance to pick up different double diffusion-driven convective flow modes, especially in the case of the fault thickness to height ratio approaching 0. (3) The significant influence of the chemical species diffusion on the convective instability of the three-dimensional geological fault zone system implies that the seawater intrusion into the surface of the Earth is a potential mechanism to trigger the convective flow in the shallow three-dimensional geological fault zone 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 (c) 2005 John Wiley & Sons, Ltd.