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Frauenrath, Tobias ; Hezel, Fabian ; Heinrichs, Uwe ; Kozerke, Sebastian ; Utting, Jane ; Kob, Malte ; Butenweg, Christoph ; Boesiger, Peter ; Niendorf, Thoralf
In order for traditional masonry to stay a competitive building material in seismically active regions there is an urgent demand for modern, deformation-based verification procedures which exploit the nonlinear load bearing reserves. The Capacity Spectrum Method (CSM) is a widely accepted design approach in the field of reinforced concrete and steel construction. It compares the seismic action with the load-bearing capacity of the building considering nonlinear material behavior with its post-peak capacity. The bearing capacity of the building is calculated iteratively using single wall capacity curves. This paper presents a new approach for the bilinear approximation of single wall capacity curves in the style of EC6/EC8 respectively FEMA 306/FEMA 356 based on recent shear wall test results of the European Collective-Research Project “ESECMaSE”. The application of the CSM to masonry structures by using bilinear approximations of capacity curves as input is demonstrated on the example of a typical German residential home.
Numerical solution of the heat equation with non-linear, time derivative-dependent source term
(2010)
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.
Quantifying and minimizing uncertainty is vital for simulating technically and economically successful geothermal reservoirs. To this end, we apply a stochastic modelling sequence, a Monte Carlo study, based on (i) creating an ensemble of possible realizations of a reservoir model, (ii) forward simulation of fluid flow and heat transport, and (iii) constraining post-processing using observed state variables. To generate the ensemble, we use the stochastic algorithm of Sequential Gaussian Simulation and test its potential fitting rock properties, such as thermal conductivity and permeability, of a synthetic reference model and—performing a corresponding forward simulation—state variables such as temperature. The ensemble yields probability distributions of rock properties and state variables at any location inside the reservoir. In addition, we perform a constraining post-processing in order to minimize the uncertainty of the obtained distributions by conditioning the ensemble to observed state variables, in this case temperature. This constraining post-processing works particularly well on systems dominated by fluid flow. The stochastic modelling sequence is applied to a large, steady-state 3-D heat flow model of a reservoir in The Hague, Netherlands. The spatial thermal conductivity distribution is simulated stochastically based on available logging data. Errors of bottom-hole temperatures provide thresholds for the constraining technique performed afterwards. This reduce the temperature uncertainty for the proposed target location significantly from 25 to 12 K (full distribution width) in a depth of 2300 m. Assuming a Gaussian shape of the temperature distribution, the standard deviation is 1.8 K. To allow a more comprehensive approach to quantify uncertainty, we also implement the stochastic simulation of boundary conditions and demonstrate this for the basal specific heat flow in the reservoir of The Hague. As expected, this results in a larger distribution width and hence, a larger, but more realistic uncertainty estimate. However, applying the constraining post-processing the uncertainty is again reduced to the level of the post-processing without stochastic boundary simulation. Thus, constraining post-processing is a suitable tool for reducing uncertainty estimates by observed state variables.