Lithium ion battery performance at high charge/discharge rates is largely determined by the ionic resistivity of an electrode and separator which are filled with electrolyte. Key to understand and to model ohmic losses in porous battery components is porosity as well as tortuosity. In the first part, we use impedance spectroscopy measurements in a new experimental setup to obtain the tortuosities and MacMullin numbers of some commonly used separators, demonstrating experimental errors of <8%. In the second part, we present impedance measurements of electrodes in symmetric cells using a blocking electrode configuration, which is obtained by using a non-intercalating electrolyte. The effective ionic resistivity of the electrode can be fit with a transmission-line model, allowing us to quantify the porosity dependent MacMullin numbers and tortuosities of electrodes with different active materials and different conductive carbon content. Best agreement between the transmission-line model and the impedance data is found when constant-phase elements rather than simple capacitors are used. Motivation.-Advanced battery models are a valuable tool for evaluating the performance, safety, and life-time of lithium ion batteries, since they can provide insight into the kinetics and the transport characteristics of batteries, which are not or only partially accessible by experiments. To obtain quantitative and meaningful numerical results, the choice of appropriate physical models and boundary conditions with the corresponding, accurately determined, kinetic and transport parameters are key issues. For numerical simulations of battery systems, the ion-transport model for concentrated electrolyte solutions introduced by Newman et al.1 is frequently used. Since the microscopic geometry of actually used porous electrodes and separators are largely unknown, a homogenization approach is applied for the macroscopic description of porous media. In this case, the influence of the microstructure on the macroscopic behavior is modeled by additional geometric parameters such as the porosity ε and the tortuosity τ. The porosity ε is a well-defined property of a porous medium, which can be determined easily. In contrast, the effective tortuosity of separators and particularly of electrodes are more difficult to quantify, and, to further complicate the matter, many different definitions for the tortuosity τ are used in the literature. Thus, the different tortuosity definitions will be presented prior to reviewing the literature concerned with determining the tortuosity or the effective ionic conductivity of porous battery separators and electrodes.

A fixed-point fluid-structure interaction (FSI) solver with dynamic relaxation is revisited. New developments and insights gained in recent years motivated us to present an FSI solver with simplicity and robustness in a wide range of applications. Particular emphasis is placed on the calculation of the relaxation parameter by both Aitken's ∆ 2 method and the method of steepest descent. These methods have shown to be crucial ingredients for efficient FSI simulations.

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SUMMARYThe coupling of flexible structures to incompressible fluids draws a lot of attention during the last decade. Many different solution schemes have been proposed. In this contribution, we concentrate on the strong coupling fluid-structure interaction by means of monolithic solution schemes. Therein, a Newton-Krylov method is applied to the monolithic set of nonlinear equations. Such schemes require good preconditioning to be efficient. We propose two preconditioners that apply algebraic multigrid techniques to the entire fluid-structure interaction system of equations. The first is based on a standard block Gauss-Seidel approach, where approximate inverses of the individual field blocks are based on a algebraic multigrid hierarchy tailored for the type of the underlying physical problem. The second is based on a monolithic coarsening scheme for the coupled system that makes use of prolongation and restriction projections constructed for the individual fields. The resulting nonsymmetric monolithic algebraic multigrid method therefore involves coupling of the fields on coarse approximations to the problem yielding significantly enhanced performance.

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