Olaf Ippisch

Modeling and simulation of two-phase two-component flow with disappearing nonwetting phase

Carbon capture and storage is a recently discussed new technology, aimed at allowing an ongoing use of fossil fuels while preventing the produced CO2 to be released to the atmosphere. CCS can be modeled with two components (water and CO2) in two phases (liquid and CO2). To simulate the process, a multiphase flow equation with equilibrium phase exchange is used. One of the big problems arising in two-phase two-component flow simulations is the disappearance of the nonwetting phase, which leads to a degeneration of the equations satisfied by the saturation. A standard choice of primary variables, which is the pressure of one phase and the saturation of the other phase, cannot be applied here. We developed a new approach using the pressure of the nonwetting phase and the capillary pressure as primary variables. One important advantage of this approach is the fact that we have only one set of primary variables that can be used for the biphasic as well as the monophasic case. We implemented this new choice of primary variables in the DUNE simulation framework and present numerical results for some test cases.

Numerical simulation and experimental studies of unsaturated water flow in heterogeneous systems

In this paper we develop higher-order Discontinuous Galerkin finite element methods for the simulation of two-phase flow in heterogeneous porous media and experimental methods to determine structure and saturation in two-dimensional Hele-Shaw cells with high resolution in space and time. Together with additional measurements of governing parameters this allows us to compare experiments with numerical simulations. Results are shown to be in good qualitative agreement.

EXA-DUNE: Flexible PDE Solvers, Numerical Methods and Applications

In the EXA-DUNE project we strive to (i) develop and implement numerical algorithms for solving PDE problems efficiently on heterogeneous architectures, (ii) provide corresponding domain-specific abstractions that allow application scientists to effectively use these methods, and (iii) demonstrate performance on porous media flow problems. In this paper, we present first results on the hybrid parallelisation of sparse linear algebra, system and RHS assembly, the implementation of multiscale finite element methods and the SIMD performance of high-order discontinuous Galerkin methods within an application scenario.

Efficient parallelization of geostatistical inversion using the quasi-linear approach

Hydraulic conductivity is a key parameter for the simulation of groundwater flow and transport. Typically, it is highly variable in space and difficult to determine by direct methods. The most common approach is to infer hydraulic-conductivity values from measurements of dependent quantities, such as hydraulic head and concentration. In geostatistical inversion, the parameters are estimated as continuous, spatially auto-correlated fields, the most likely values of which are obtained by conditioning on the indirect data. In order to identify small-scaled features, a fine three-dimensional discretization of the domain is needed. This leads to high computational demands in the solution of the forward problem and the calculation of sensitivities. In realistic three-dimensional settings with many measurements parallel computing becomes mandatory. In the present study, we investigate how parallelization of the quasi-linear geostatistical approach of inversion can be made most efficient. We suggest a two-level approach of parallelization, in which the computational domain is subdivided and the evaluation of sensitivities is also parallelized. We analyze how these two levels of parallelization should be balanced to optimally exploit a given number of computing nodes.

An Unfitted Discontinuous Galerkin method for pore-scale simulations of solute transport

Abstract: For the simulation of transport processes in porous media effective parameters for the physical processes on the target scale are required. Numerical upscaling, as well as multiscale approaches can help where experiments are not possible, or hard to conduct. In 2009, Bastian and Engwer proposed an Unfitted Discontinuous Galerkin (UDG) method for solving PDEs in complex domains, e.g. on the pore scale. We apply this method to a parabolic test problem. Convergence studies show the expected second order convergence. As an application example solute transport in a porous medium at the pore scale is simulated. Macroscopic breakthrough curves are computed using direct simulations. The method allows finite element meshes which are significantly coarser then those required by standard conforming finite element approaches. Thus it is possible to obtain reliable numerical results for macroscopic parameter already for a relatively coarse grid.

Hardware-Based Efficiency Advances in the EXA-DUNE Project

We present advances concerning efficient finite element assembly and linear solvers on current and upcoming HPC architectures obtained in the frame of the Exa-Dune project, part of the DFG priority program 1648 Software for Exascale Computing (SPPEXA). In this project, we aim at the development of both flexible and efficient hardware-aware software components for the solution of PDEs based on the DUNE platform and the FEAST library. In this contribution, we focus on node-level performance and accelerator integration, which will complement the proven MPI-level scalability of the framework. The higher-level aspects of the Exa-Dune project, in particular multiscale methods and uncertainty quantification, are detailed in the companion paper (Bastian et al., Advances concerning multiscale methods and uncertainty quantification in Exa-Dune. In: Proceedings of the SPPEXA Symposium, 2016).

Advances Concerning Multiscale Methods and Uncertainty Quantification in EXA-DUNE

In this contribution we present advances concerning efficient parallel multiscale methods and uncertainty quantification that have been obtained in the frame of the DFG priority program 1648 Software for Exascale Computing (SPPEXA) within the funded project Exa-Dune. This project aims at the development of flexible but nevertheless hardware-specific software components and scalable high-level algorithms for the solution of partial differential equations based on the DUNE platform. While the development of hardware-based concepts and software components is detailed in the companion paper (Bastian et al., Hardware-based efficiency advances in the Exa-Dune project. In: Proceedings of the SPPEXA Symposium 2016, Munich, 25–27 Jan 2016), we focus here on the development of scalable multiscale methods in the context of uncertainty quantification. Such problems add additional layers of coarse grained parallelism, as the underlying problems require the solution of many local or global partial differential equations in parallel that are only weakly coupled.

Tomographic Methods in Hydrogeology

The extraction of groundwater for drinking water purposes is one of the most important uses of the natural subsurface. Sustainable management of groundwater resources requires detailed knowledge of the hydraulic properties within the subsurface. Typically, these properties are not directly accessible. The evaluation of hydraulic properties therefore requires hydraulic stimuli of the subsurface (e.g., injection and extraction of groundwater, tracer tests, etc.) with subsequent data analysis. In this context, tomographic techniques and inversion strategies originally derived for geophysical surveying can be transferred to hydraulic applications. In addition, geophysical techniques may be used to monitor hydraulic tests. The latter requires fully coupled hydrogeophysical inversion strategies, accounting for the entire process chain from hydraulic properties via flow and transport to the application of the geophysical surveying techniques. The project “Tomographic methods in hydrogeology” focuses on the development of a geostatistical inversion method for transient tomographic data of multiple hydraulic investigation techniques, the model-based optimal design of tomographic surveys, and the development of experimental techniques and equipment for an efficient execution of tomographic surveys in a hydrogeological context using the model-based design and providing data for the inversion. In this chapter we will show selected examples of the project’s outcome. The examples include developments related to the joint geostatistical inversion of tomographic data sets, its efficient parallelization, and its application to a 3D-inversion of tomographic thermal tracer tests. Furthermore we present a method for solving the inversion of transient tomographic data sets which usually suffer from high computational efforts. Related to the acquisition of tomographic data sets, we also discuss the development of tracer-tomographic methods using heat as tracer.

Benchmark 3D: A Mimetic Finite Difference Method

In the two-dimensional discretisation benchmark session at the FVCA5 conference, we participated with a Mimetic Finite Difference (MFD) method [7]. In this paper, we present results for the three-dimensional case using the same method. Since the previous conference, the equivalence of MFD, Hybrid Finite Volume and Mixed Finite Volume methods has been demonstrated in [6]. Our outline of the method as used in our computations follows the exposition in [5].

Hydraulic Parameter Estimation in Heterogeneous Porous Media

The determination of hydraulic parameter functions is crucial for the modeling of multiphase flow in porous media. The combination of multistep-outflow experiments and inverse modeling is a standard method for the determination of hydraulic properties for unsaturated flow. Up to now it is necessary to assume, that the sample is homogeneous, which is not true for most natural porous media. Measurement techniques like x-ray tomography, geoelectrics and georadar allow the non-destructive determination of the spatial structure of a sample. If thus the structure of a sample is known, it can be possible to estimate the hydraulic property functions of the basic materials of a soil with multistep-outflow experiments and an optimisation procedure, which takes the structure explicitly into account. A code for parameter optimisation in 2D and 3D structured material is presented and applied to experimental data. The estimated hydraulic parameters for homogeneous and heterogeneous samples are compared.