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W. K. van Wijngaarden F. J. Vermolen G. A. M. van Meurs C. Vuik 《Computational Geosciences》2013,17(3):463-478
We present a mathematical model for Biogrout, which is a technique for soil reinforcement that is based on microbially induced carbonate precipitation. The model deals with the entire process, consisting of fixation of bacteria, as well as of the subsequent soil reinforcement. The paper deals with the coupling of two earlier models for bacterial placement and reinforcement, where the construction of the model is discussed, as well as numerical results. Further, we present analytical solutions for the constant flow velocity case. The model is based on the assumption that the porous medium is stiff. 相似文献
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Dynamic two‐phase interaction of soil can be modelled by a displacement‐based, two‐phase formulation. The finite element method together with a semi‐implicit Euler–Cromer time‐stepping scheme renders a discrete equation that can be solved by recursion. By experience, it is found that the CFL stability condition for undrained wave propagation is not sufficient for the considered two‐phase formulation to be numerically stable at low values of permeability. Because the stability analysis of the two‐phase formulation is onerous, an analysis is performed on a simplified two‐phase formulation that is derived by assuming an incompressible pore fluid. The deformation of saturated porous media is now captured in a single, second‐order partial differential equation, where the energy dissipation associated with the flow of the fluid relative to the soil skeleton is represented by a damping term. The paper focuses on the different options to discretize the damping term and its effect on the stability criterion. Based on the eigenvalue analyses of a single element, it is observed that in addition to the CFL stability condition, the influence of the permeability must be included. This paper introduces a permeability‐dependent stability criterion. The findings are illustrated and validated with an example for the dynamic response of a sand deposit. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Accurate simulation of fluid pressures in layered reservoirs with strong permeability contrasts is a challenging problem. For this purpose, the Discontinuous Galerkin (DG) method has become increasingly popular. Unfortunately, standard linear solvers are usually too inefficient for the aforementioned application. To increase the efficiency of the conjugate gradient (CG) method for linear systems resulting from symmetric interior penalty (discontinuous) Galerkin (SIPG) discretizations, we cast an existing two-level preconditioner into the deflation framework. The main idea is to use coarse corrections based on the DG solution with polynomial degree p = 0. This paper provides a numerical comparison of the performance of the original preconditioner and the resulting deflation variant in terms of scalability and overall efficiency. Furthermore, it studies the influence of the SIPG penalty parameter, weighted averages in the SIPG formulation (SWIP), the smoother, damping of the smoother, and the strategy for solving the coarse systems. We have found that the penalty parameter can best be chosen diffusion-dependent. In that case, both two-level methods yield fast and scalable convergence. Whether preconditioning or deflation is to be favored depends on the choice of the smoother and on the damping of the smoother. Altogether, both two-level methods can contribute to cheaper and more accurate fluid pressure simulations. 相似文献
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In geophysical applications, the interest in least-squares migration (LSM) as an imaging algorithm is increasing due to the demand for more accurate solutions and the development of high-performance computing. The computational engine of LSM in this work is the numerical solution of the 3D Helmholtz equation in the frequency domain. The Helmholtz solver is Bi-CGSTAB preconditioned with the shifted Laplace matrix-dependent multigrid method. In this paper, an efficient LSM algorithm is presented using several enhancements. First of all, a frequency decimation approach is introduced that makes use of redundant information present in the data. It leads to a speedup of LSM, whereas the impact on accuracy is kept minimal. Secondly, a new matrix storage format Very Compressed Row Storage (VCRS) is presented. It not only reduces the size of the stored matrix by a certain factor but also increases the efficiency of the matrix-vector computations. The effects of lossless and lossy compression with a proper choice of the compression parameters are positive. Thirdly, we accelerate the LSM engine by graphics cards (GPUs). A GPU is used as an accelerator, where the data is partially transferred to a GPU to execute a set of operations or as a replacement, where the complete data is stored in the GPU memory. We demonstrate that using the GPU as a replacement leads to higher speedups and allows us to solve larger problem sizes. Summarizing the effects of each improvement, the resulting speedup can be at least an order of magnitude compared to the original LSM method. 相似文献
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Diaz Cortés Gabriela Berenice Vuik Cornelis Jansen Jan-Dirk 《Computational Geosciences》2021,25(5):1621-1645
We explore and develop a Proper Orthogonal Decomposition (POD)-based deflation method for the solution of ill-conditioned linear systems, appearing in simulations of two-phase flow through highly heterogeneous porous media. We accelerate the convergence of a Preconditioned Conjugate Gradient (PCG) method achieving speed-ups of factors up to five. The up-front extra computational cost of the proposed method depends on the number of deflation vectors. The POD-based deflation method is tested for a particular problem and linear solver; nevertheless, it can be applied to various transient problems, and combined with multiple solvers, e.g., Krylov subspace and multigrid methods.
相似文献6.
A robust method to tackle pressure boundary conditions in porous media flow: application to biogrout
W. K. van Wijngaarden F. J. Vermolen G. A. M. van Meurs C. Vuik 《Computational Geosciences》2014,18(2):103-115
Biogrout is a soil improvement method in which microorganisms are used to produce the solid calcium carbonate, which strengthens the soil by connecting soil particles. Microorganisms in the soil are supplied with some nutrients, which they convert into calcium carbonate. These nutrients and the side product of the reaction are dissolved in water. Because of these chemicals, the fluid is denser than water. Moreover, the density changes as a result of the varying composition. This changing density has a significant impact on the flow. Since the composition and hence, the density is not known beforehand, a careful choice of the (pressure) boundary conditions, especially on the outflow boundary, is needed. In this article, several methods to approximate the pressure on the outflow boundary are compared. The method that we propose also works for an unstructured mesh, which gives a large freedom in the mesh generation. 相似文献
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