In this paper we provide a general framework for model reduction methods applied to fluid flow in porous media. Using reduced basis and numerical homogenization techniques we show that the complexity of the numerical ...
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ISBN:
(纸本)9783319399294;9783319399270
In this paper we provide a general framework for model reduction methods applied to fluid flow in porous media. Using reduced basis and numerical homogenization techniques we show that the complexity of the numerical approximation of Stokes flow in heterogeneous media can be drastically reduced. The use of such a computational framework is illustrated at several model problems such as two and three scale porous media.
Optimization algorithms typically perform a series of function evaluations to find an approximation of an optimal point of the objective function. Evaluations can be expensive, e. g., if they depend on the results of ...
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ISBN:
(数字)9783319282626
ISBN:
(纸本)9783319282626;9783319282602
Optimization algorithms typically perform a series of function evaluations to find an approximation of an optimal point of the objective function. Evaluations can be expensive, e. g., if they depend on the results of a complex simulation. When dealing with higher-dimensional functions, the curse of dimensionality increases the difficulty of the problem rapidly and prohibits a regular sampling. Instead of directly optimizing the objective function, we replace it with a sparse grid interpolant, saving valuable function evaluations. We generalize the standard piecewise linear basis to hierarchical B-splines, making the sparse grid surrogate smooth enough to enable gradient-based optimization methods. Also, we use an uncommon refinement criterion due to Novak and Ritter to generate an appropriate sparse grid adaptively. Finally, we evaluate the new method for various artificial and real-world examples.
We present a mathematical and numerical model for non-isothermal, compressible flow of a mixture of two ideal gases subject to gravity. This flow is described by the balance equations for mass, momentum and energy tha...
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ISBN:
(纸本)9783319399294;9783319399270
We present a mathematical and numerical model for non-isothermal, compressible flow of a mixture of two ideal gases subject to gravity. This flow is described by the balance equations for mass, momentum and energy that are solved numerically by the scheme based on themethod of lines. The spatial discretization is carried out by means of the finite volume method, where the staggered arrangement of variables is employed. The time integration is realized by the Runge-KuttaMerson method. The article also contains test results obtained by the presented
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