Math2Market GmbH

Kaiserslautern, Germany

Math2Market GmbH

Kaiserslautern, Germany
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Linden S.,University of Kaiserlautern | Linden S.,Fraunhofer Institute for Industrial Mathematics | Hagen H.,University of Kaiserlautern | Wiegmann A.,Math2Market GmbH
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2014

We introduce a novel multi-dimensional space partitioning method. A new type of tree combines the advantages of the Octree and the KD-tree without having their disadvantages. We present in this paper a new data structure allowing local refinement, parallelization and proper restriction of transition ratios between cells. Our technique has no dimensional restrictions at all. The tree's data structure is defined by a topological algebra based on the symbols A = {L, I, R} that encode the partitioning steps. The set of successors is restricted such that each cell has the partition of unity property to partition domains without overlap. With our method it is possible to construct a wide choice of spline spaces to compress or reconstruct scientific data such as pressure and velocity fields and multidimensional images. We present a generator function to build a tree that represents a voxel geometry. The space partitioning system is used as a framework to allow numerical computations. This work is triggered by the problem of representing, in a numerically appropriate way, huge three-dimensional voxel geometries that could have up to billions of voxels. © Springer-Verlag 2014.

Maus S.,University of Bergen | Leisinger S.,Swiss Federal Institute of forest | Matzl M.,Swiss Federal Institute of forest | Schneebeli M.,Swiss Federal Institute of forest | Wiegmann A.,Math2Market GmbH
Proceedings of the International Conference on Port and Ocean Engineering under Arctic Conditions, POAC | Year: 2013

Oil entrapment in drifting sea ice may lead to release of oil far away from spilling locations, when the ice finally melts at the end of its drift. The entrapment process hence needs to be understood properly to evaluate the environmental risks of oil spills in ice-covered waters. However, field studies of oil-in-ice processes are sparse, while laboratory tests do not necessarily represent natural sea ice in terms of growth conditions, time scales and, in particular, microstructures. In this study we consider the role that the microstructure of sea ice may play for oil entrapment. We discuss oil migration into the sea ice pore space on the basis of 3-d images of young winter sea ice, obtained by X-ray micro-tomography. Simulating fluid flow through these images we obtain the vertical distribution of sea ice permeability and pore size distributions, the basic parameter for the prediction of migration of oil into the ice. We compare the analysis with published results from laboratory experiments of oil entrapment in laboratory-grown ice of similar age. Our analysis suggests that care must be taken when interpreting laboratory experiments, due to limited oil amounts released. Furthermore, we perform a similar analysis of older and thicker summer ice that has similar porosity yet coarser pores. The potential of the old ice to entrap oil is expected to be an order of magnitude larger than indicated by results with young laboratory-grown ice. Due to the importance of sea ice microstructure to predict oil entrapment and transport, future approaches should include models of sea ice microstructure evolution with growth and melt conditions.

Kling T.,Karlsruhe Institute of Technology | Huo D.,Stanford University | Schwarz J.O.,Johannes Gutenberg University Mainz | Schwarz J.O.,Math2Market GmbH | And 3 more authors.
Solid Earth | Year: 2016

Various geoscientific applications require a fast prediction of fracture permeability for an optimal workflow. Hence, the objective of the current study is to introduce and validate a practical method to characterize and approximate single flow in fractures under different stress conditions by using a core-flooding apparatus, in situ X-ray computed tomography (CT) scans and a finite-volume method solving the Navier-Stokes-Brinkman equations. The permeability of the fractured sandstone sample was measured stepwise during a loading-unloading cycle (0.7 to 22.1MPa and back) to validate the numerical results. Simultaneously, the pressurized core sample was imaged with a medical X-ray CT scanner with a voxel dimension of 0.5 × 0.5 × 1.0mm3. Fracture geometries were obtained by CT images based on a modification of the simplified missing attenuation (MSMA) approach. Simulation results revealed both qualitative plausibility and a quantitative approximation of the experimentally derived permeabilities. The qualitative results indicate flow channeling along several preferential flow paths with less pronounced tortuosity. Significant changes in permeability can be assigned to temporal and permanent changes within the fracture due to applied stresses. The deviations of the quantitative results appear to be mainly caused by both local underestimation of hydraulic properties due to compositional matrix heterogeneities and the low CT resolution affecting the accurate capturing of sub-grid-scale features. Both affect the proper reproduction of the actual connectivity and therefore also the depiction of the expected permeability hysteresis. Furthermore, the threshold value CTmat (1862.6HU) depicting the matrix material represents the most sensitive input parameter of the simulations. Small variations of CTmat can cause enormous changes in simulated permeability by up to a factor of 2.6±0.1 and, thus, have to be defined with caution. Nevertheless, comparison with further CT-based flow simulations indicates that the proposed method represents a valuable method to approximate actual permeabilities, particularly for smooth fractures (<35μm). However, further systematic investigations concerning the applicability of the method are essential for future studies. Thus, some recommendations are compiled by also including suggestions of comparable studies. © 2016 Author(s).

Maus S.,Norwegian University of Science and Technology | Becker J.,Math2Market GmbH | Leisinger S.,3WSL Swiss Federal Institute for Snow and Avalanche Research | Matzl M.,3WSL Swiss Federal Institute for Snow and Avalanche Research | And 2 more authors.
Proceedings of the International Conference on Port and Ocean Engineering under Arctic Conditions, POAC | Year: 2015

Observations have shown that oil spilled under sea ice collects in patches within the under-ice relief and is encapsulated in the growing ice sheet. Due to its lower density, compared to seawater brine, oil will migrate upwards into the sea ice pore space. During winter migration is limited to lower levels where pore sizes and porosity are larger than near the colder ice surface. Upon warming the oil may continue migration through the widening pore network. To predict when oil may reach the surface, good information about oil saturation, the fraction of the sea ice pore space that may be occupied by oil, is needed. However, at present little is known about the influence on oil saturation and its dependence on sea ice porosity and microstructure. Here we analyse a recently obtained dataset of 3-d X-ray micro-tomographic images of young sea ice to determine oil saturation. We use these images to perform numerical simulations of the immiscible displacement of brine (wetting fluid) by oil (non-wetting) and thereby determine the dependence of oil saturation on porosity and capillary pressure/oil patch thickness. Comparing the results to published observations of laboratory-grown seawater ice of similar age highlights the importance of internal convection for oil entrainment. We perform the analysis for a limited set of 3-d images of older first-year ice of similar porosity. The comparison suggests one to two order higher oil saturation and oil storage capacity in the old ice. To determine the seasonal evolution in the saturation-porosity relationship of oil in sea ice during aging, more observations are needed. This relationship is crucial to estimate the porosity-dependent storage capacity of oil in sea ice, predict oil surfacing, and will be important for planning of response scenarios to oil spills under sea ice.

Janousch C.,Aalen University of Applied Sciences | Winkler R.,Aalen University of Applied Sciences | Wiegmann A.,Math2Market GmbH | Pannert W.,Aalen University of Applied Sciences | And 2 more authors.
Materialwissenschaft und Werkstofftechnik | Year: 2014

Customers nowadays regard the noise and vibration behavior as an essential product property. Cellular character materials, in particular hollow sphere structures, are predestined to absorb sound in a very efficient manner due to their cellular character. Depending on the constituent material, the geometric parameters like the diameter of the spheres, the thickness of the walls and the assembling schema of single spheres, the absorption coefficient can be reduced to very low levels. In contrast to other cellular materials, the frequency and bandwidth can actively be influenced by the variation of the above mentioned parameters. In order to predict the acoustic behavior of a structure, FE or CFD analyses are used as standard tools. In addition, there exist some parameter based models, e.g. the BIOT theory, which characterizes the absorption, transmission and reflection coefficients using a few macroscopic parameters. Within this contribution, the acoustic properties of hollow sphere structures are investigated by a so-called virtual material laboratory GeoDict (by Math2Market GmbH, originally by the Fraunhofer Institute for Industrial Mathematics). The results for the absorption and reflection coefficients are compared to those gained by classical analysis methods and experiments based on Kundt's tube. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Fallet A.,Constellium | Lhuissier P.,French National Center for Scientific Research | Salvo L.,French National Center for Scientific Research | Martin C.L.,French National Center for Scientific Research | And 2 more authors.
Scripta Materialia | Year: 2013

Random hollow sphere stackings present good performance for the seemingly contradictory requirements of a light structural material and good acoustic damping properties. A way to optimize the architectured materials parameters is described. The structural properties of random hollow sphere stacking have been measured using X-ray tomography and compared to an Artz compaction model. The mechanical properties are optimized according to the architectural parameters by way of coupled finite elements and discrete elements simulations, and acoustical properties are discussed based on tube absorption models. © 2012 Published by Elsevier Ltd.

Berg S.,Royal Dutch Shell | Rucker M.,Royal Dutch Shell | Rucker M.,Johannes Gutenberg University Mainz | Ott H.,Royal Dutch Shell | And 9 more authors.
Advances in Water Resources | Year: 2016

Pore-scale images obtained from a synchrotron-based X-ray computed micro-tomography (μCT) imbibition experiment in sandstone rock were used to conduct Navier-Stokes flow simulations on the connected pathways of water and oil phases. The resulting relative permeability was compared with steady-state Darcy-scale imbibition experiments on 5. cm large twin samples from the same outcrop sandstone material. While the relative permeability curves display a large degree of similarity, the endpoint saturations for the μCT data are 10% in saturation units higher than the experimental data. However, the two datasets match well when normalizing to the mobile saturation range. The agreement is particularly good at low water saturations, where the oil is predominantly connected. Apart from different saturation endpoints, in this particular experiment where connected pathway flow dominates, the discrepancies between pore-scale connected pathway flow simulations and Darcy-scale steady-state data are minor overall and have very little impact on fractional flow. The results also indicate that if the pore-scale fluid distributions are available and the amount of disconnected non-wetting phase is low, quasi-static flow simulations may be sufficient to compute relative permeability. When pore-scale fluid distributions are not available, fluid distributions can be obtained from a morphological approach, which approximates capillary-dominated displacement. The relative permeability obtained from the morphological approach compare well to drainage steady state whereas major discrepancies to the imbibition steady-state experimental data are observed. The morphological approach does not represent the imbibition process very well and experimental data for the spatial arrangement of the phases are required. Presumably for modeling imbibition relative permeability an approach is needed that captures moving liquid-liquid interfaces, which requires viscous and capillary forces simultaneously. © 2016 The Authors.

Cheng L.,Math2Market GmbH | Becker J.,Math2Market GmbH | Kronsbein C.,Math2Market GmbH | Westerteiger R.,Math2Market GmbH | Wiegmann A.,Math2Market GmbH
American Filtration and Separations Society Fall Conference 2015, AFS 2015: Advanced Technologies in Filter Media | Year: 2015

Understanding existing and designing new air filter media is a recurring task for academics as well as industrial researchers. One approach to this task is to use trial and error in modeling and simulation rather than trial and error in real experiments. Both the media and the filter design play a crucial role for the performance of the filter. Here, the focus is on the details of fibrous filter media. One can try to understand them by performing detailed 3-dimensional simulations of the filter media, air flow, particle motion, particle capture and filter clogging. The first task is to create a geometric model of the filter media in the computer. This can be achieved using SEM or ideally μCT images of the filter media. After image enhancement and segmentation, a 3d array of millions of solid and empty cubic cells is created. On such an array, filtration process simulations can be performed but they are not feasible to modify in a media design step. Instead, geometric properties such as porosity, fiber diameters, fiber orientation, etc. must be determined and then converted into computable structures like the one from μCT. To achieve this, automatic algorithms to determine porosity, local orientation and local fiber diameters were developed. We compare filtration performance simulations on segmented μCT scans, media modelled after these and physical experiments with good agreement.

Linden S.,Math2Market GmbH | Hagen H.,University of Kaiserslautern | Wiegmann A.,Math2Market GmbH
76th European Association of Geoscientists and Engineers Conference and Exhibition 2014: Experience the Energy - Incorporating SPE EUROPEC 2014 | Year: 2014

We introduce a novel approach to compute the permeability on very large CT images of core samples. The LIR-tree is used for spatial partitioning of the geometry. The images are coarsened in areas where the velocity and pressure do not vary much while keeping the original resolution near the solid surfaces. In addition, solid regions do not occupy computational memory. Variables are arranged in a way such that each cell is able to satisfy the Stokes-equations independently from its neighbor cells. Pressure and velocity are discretized on staggered grids but instead of using one velocity variable on the cell faces we introduce two velocity variables. They discretize the two one-sided limits at the center of the cell surface. The discretization of the momentum and mass conservation equations yields one small linear system per cell. This structure allows to use the block Gauß-Seidel-algorithm as iterative solver. We compare our method to three other solvers on a large complex Berea sandstone dataset. The method is 3-6 times faster, scales well for up to 32 processors and has very low memory requirements. An additional benefit of this work is that the range of permeabilities from the benchmark can be narrowed down significantly.

Linden S.,Math2Market GmbH | Linden S.,Fraunhofer Institute for Industrial Mathematics | Wiegmann A.,Math2Market GmbH | Hagen H.,University of Kaiserslautern
Graphical Models | Year: 2015

We introduce a novel approach to solve the stationary Stokes equations on very large voxel geometries. One main idea is to coarsen a voxel geometry in areas where velocity does not vary much while keeping the original resolution near the solid surfaces. For spatial partitioning a simplified LIR-tree is used which is a generalization of the Octree and KD-tree. The other main idea is to arrange variables in a way such that each cell is able to satisfy the Stokes equations independently. Pressure and velocity are discretized on staggered grids. But instead of using one velocity variable on the cell surface we introduce two variables. The discretization of momentum and mass conservation yields a small linear system (block) per cell that allows to use the block Gauss-Seidel algorithm as iterative solver. We compare our method to other solvers and conclude superior performance in runtime and memory for high porosity geometries. © 2015 Elsevier Inc.

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