Partitioned semi-implicit methods for simulation of biomechanical fluid-structure interaction problems

This article is published under a CC BY licence. The Version of Record is available online at: http://dx.doi.org/10.1088/1742-6596/745/3/032020.This paper represents numerical simulation of fluid-structure interaction (FSI) system involving an incompressible viscous fluid and a lightweight elastic structure. We follow a semi-implicit approach in which we implicitly couple the added-mass term (pressure stress) of the fluid to the structure, while other terms are coupled explicitly. This significantly reduces the computational cost of the simulations while showing adequate stability. Several coupling schemes are tested including fixed-point method with different static and dynamic relaxation, as well as Newton-Krylov method with approximated Jacobian. Numerical tests are conducted in the context of a biomechanical problem. Results indicate that the Newton-Krylov solver outperforms fixed point ones while introducing more complexity to the problem due to the evaluation of the Jacobian. Fixed-point solver with Aitken's relaxation method also proved to be a simple, yet efficient method for FSI simulations.Peer ReviewedPostprint (published version

Numerical Simulations of the Dark Universe: State of the Art and the Next Decade

We present a review of the current state of the art of cosmological dark matter simulations, with particular emphasis on the implications for dark matter detection efforts and studies of dark energy. This review is intended both for particle physicists, who may find the cosmological simulation literature opaque or confusing, and for astro-physicists, who may not be familiar with the role of simulations for observational and experimental probes of dark matter and dark energy. Our work is complementary to the contribution by M. Baldi in this issue, which focuses on the treatment of dark energy and cosmic acceleration in dedicated N-body simulations. Truly massive dark matter-only simulations are being conducted on national supercomputing centers, employing from several billion to over half a trillion particles to simulate the formation and evolution of cosmologically representative volumes (cosmic scale) or to zoom in on individual halos (cluster and galactic scale). These simulations cost millions of core-hours, require tens to hundreds of terabytes of memory, and use up to petabytes of disk storage. The field is quite internationally diverse, with top simulations having been run in China, France, Germany, Korea, Spain, and the USA. Predictions from such simulations touch on almost every aspect of dark matter and dark energy studies, and we give a comprehensive overview of this connection. We also discuss the limitations of the cold and collisionless DM-only approach, and describe in some detail efforts to include different particle physics as well as baryonic physics in cosmological galaxy formation simulations, including a discussion of recent results highlighting how the distribution of dark matter in halos may be altered. We end with an outlook for the next decade, presenting our view of how the field can be expected to progress. (abridged)Comment: 54 pages, 4 figures, 3 tables; invited contribution to the special issue "The next decade in Dark Matter and Dark Energy" of the new Open Access journal "Physics of the Dark Universe". Replaced with accepted versio

Modelling of impulse loading in high-temperature superconductors. Assessment of accuracy and performance of computational techniques.

Purpose – The aim of this paper is to access performance of existing computational techniques to model strongly non-linear field diffusion problems. Design/methodology/approach – Multidimensional application of a finite volume front-fixing method to various front-type problems with moving boundaries and non-linear material properties is discussed. Advantages and implementation problems of the technique are highlighted by comparing the front-fixing method with computations using fixed grids. Particular attention is focused on conservation properties of the algorithm and accurate solutions close to the moving boundaries. The algorithm is tested using analytical solutions of diffusion problems with cylindrical symmetry with both spatial and temporal accuracy analysed. Findings – Several advantages are identified in using a front-fixing method for modelling of impulse phenomena in high-temperature superconductors (HTS), namely high accuracy can be obtained with a small number of grid points, and standard numerical methods for convection problems with diffusion can be utilised. Approximately, first order of spatial accuracy is found for all methods (stationary or mobile grids) for 2D problems with impulse events. Nevertheless, errors resulting from a front-fixing technique are much smaller in comparison with fixed grids. Fractional steps method is proved to be an effective algorithm for solving the equations obtained. A symmetrisation procedure has to be introduced to eliminate a directional bias for a standard asymmetric split in diffusion processes. Originality/value – This paper for the first time compares in detail advantages and implementation complications of a front-fixing method when applied to the front-type field diffusion problems common to HTS. Particular attention is paid to accurate solutions in the region close to the moving front where rapid changes in material properties are responsible for large computational errors. Keywords - Modelling, Numerical analysis, Diffusion, High temperatures, Superconductors Paper type - Research pape