A One-Field Monolithic Fictitious Domain Method for Fluid-Structure Interactions

In this article, we present a one- eld monolithic fictitious domain (FD) method for simulation of general fluid-structure interactions (FSI). "One-fi eld" means only one velocity field is solved in the whole domain, based upon the use of an appropriate L2 projection. "Monolithic" means the fluid and solid equations are solved synchronously (rather than sequentially). We argue that the proposed method has the same generality and robustness as FD methods with distributed Lagrange multiplier (DLM) but is signi ficantly more computationally e fficient (because of one-fi eld) whilst being very straightforward to implement. The method is described in detail, followed by the presentation of multiple computational examples in order to validate it across a wide range of fluid and solid parameters and interactions

A Cache-Aware Approach to Domain Decomposition for Stencil-Based Codes

Partial Differential Equations (PDEs) lie at the heart of numerous scientific simulations depicting physical phenomena. The parallelization of such simulations introduces additional performance penalties in the form of local and global synchronization among cooperating processes. Domain decomposition partitions the largest shareable data structures into sub-domains and attempts to achieve perfect load balance and minimal communication. Up to now research efforts to optimize spatial and temporal cache reuse for stencil-based PDE discretizations (e.g. finite difference and finite element) have considered sub-domain operations after the domain decomposition has been determined. We derive a cache-oblivious heuristic that minimizes cache misses at the sub-domain level through a quasi-cache-directed analysis to predict families of high performance domain decompositions in structured 3-D grids. To the best of our knowledge this is the first work to optimize domain decompositions by analyzing cache misses - thus connecting single core parameters (i.e. cache-misses) to true multicore parameters (i.e. domain decomposition). We analyze the trade-offs in decreasing cache-misses through such decompositions and increasing the dynamic bandwidth-per-core. The limitation of our work is that currently, it is applicable only to structured 3-D grids with cuts parallel to the Cartesian Axes. We emphasize and conclude that there is an imperative need to re-think domain decompositions in this constantly evolving multicore era

Jetting behavior in drop-on-demand printing: Laboratory experiments and numerical simulations

The formation and evolution of micron-sized droplets of a Newtonian liquid generated on demand in an industrial inkjet printhead are studied experimentally and simulated numerically. The shapes and positions of droplets during droplet formation are observed using a high-speed camera and compared with their numerically obtained analogs. Both the experiments and the simulations use practical length scales for inkjet printing. The results show how fluid properties, specifically viscosity and surface tension, affect the drop formation, ligament length, and breakoff time. We identify the parameter space of fluid properties for producing single drops at a prescribed speed and show this is not simply a restriction on the Ohnesorge number, but that there is an additional restriction on the Reynolds number that is distinct from the Reynolds number limit associated with the prevention of splashing. This phase diagram provides more precise guidance on the space of fluid parameters for jetting single droplets in drop-on-demand inkjet printers

An efficient numerical algorithm for a multiphase tumour model

This paper is concerned with the development and application of optimally efficient numerical methods for the simulation of vascular tumour growth. This model used involves the flow and interaction of four different, but coupled, phases which are each treated as incompressible fluids, Hubbard and Byrne (2013). A finite volume scheme is used to approximate mass conservation, with conforming finite element schemes to approximate momentum conservation and an associated equation. The principal contribution of this paper is the development of a novel block preconditioner for solving the linear systems arising from the discrete momentum equations at each time step. In particular, the preconditioned system has both a solution time and a memory requirement that is shown to scale almost linearly with the problem size

Mathematical Modelling of Chemical Diffusion through Skin using Grid-based PSEs

A Problem Solving Environment (PSE) with connections to remote distributed Grid processes is developed. The Grid simulation is itself a parallel process and allows steering of individual or multiple runs of the core computation of chemical diffusion through the stratum corneum, the outer layer of the skin. The effectiveness of this Grid-based approach in improving the quality of the simulation is assessed

A Cache-Aware Approach to Adaptive Mesh Refinement in Parallel Stencil-based Solvers

In prior-research the authors have demonstrated that, for stencil-based numerical solvers for Partial Differential Equations (PDEs), the parallel performance can be significantly improved by selecting sub-domains that are not cubic in shape (Saxena et. al., HPCS 2016, pp. 875-885). This is achieved through accounting for cache utilization in both the message passing and the computational kernel, where it is demonstrated that the optimal domain decompositions not only depend on the communication and load balance but also on the cache-misses, amongst other factors. In this work we demonstrate that those conclusions may also be extended to more advanced numerical discretizations, based upon Adaptive Mesh Refinement (AMR). In particular, we show that when basing our AMR strategy on the local refinement of patches of the mesh, the optimal patch shape is not typically cubic. We provide specific examples, with accompanying explanation, to show that communication minimizing strategies are not necessarily the best choice when applying AMR in parallel. All numerical tests undertaken in this work are based upon the open source BoxLib library

Anisotropic mechanical response of layered disordered fibrous materials

Mechanically bonded fabrics account for a significant portion of nonwoven products, and serve many niche areas of nonwoven manufacturing. Such fabrics are characterized by layers of disordered fibrous webs, but we lack an understanding of how such microstructures determine bulk material response. Here we numerically determine the linear shear response of needle-punched fabrics modeled as cross-linked sheets of two-dimensional (2D) Mikado networks. We systematically vary the intra-sheet fiber density, inter-sheet separation distance, and direction of shear, and quantify the macroscopic shear modulus alongside the degree of affinity and energy partition. For shear parallel to the sheets, the response is dominated by intrasheet fibers and follows known trends for 2D Mikado networks. By contrast, shears perpendicular to the sheets induce a softer response dominated by either intrasheet or intersheet fibers depending on a quadratic relation between sheet separation and fiber density. These basic trends are reproduced and elucidated by a simple scaling argument that we provide. We discuss the implications of our findings in the context of real nonwoven fabrics

Impact of calcium hydroxide on physical characteristics and leaching stability of metakaolin-based geopolymer waste form containing radioactive borate waste

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A Study of Preconditioned Jacobian-Free Newton-Krylov Discontinuous Galerkin Method for Compressible Flows on 3D Hexahedral Grids

Storage requirement and computational efficiency have always been challenges for the efficient implementation of discontinuous Galerkin (DG)methods for real life applications. In this paper, a fully implicit Jacobian-Free Newton-Krylov (JFNK) method is developed in the context of DG discretizations for the three-dimensional compressible Euler and Navier-Stokes equations. Compared with the Jacobian-based methods, the Jacobian-Free approach saves the storage for the Jacobian matrix which can be of great importance for DG methods. Three types of preconditioners are investigated in which the block diagonal preconditioner requires the least storage, while the block LU-SGS and ILU0 preconditioners require more storage but are more computationally efficient. An implicit time-stepping strategy is adopted for the stability of the current solver,which is based upon a hexahedral spatialmesh and the nonlinear solver package Kinsol is used to improve the computational efficiency and robustness. Numerical results demonstrate that the preconditioned JFNK-DG solver can substantially reduce the storage requirement compared with the Jacobian based method without significantly compromising accuracy or efficiency. Furthermore, as a good compromise between efficiency and storage requirement, the ILU0 preconditioner shows the best choice of the preconditioners presented