A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3,700 are used to verify the accuracy and physical fidelity of the formulation.Comment: 32 pages, 9 figures; preprint submitted to Journal of Computational Physic

Investigation of mixed element hybrid grid-based CFD methods for rotorcraft flow analysis

Accurate first-principles flow prediction is essential to the design and development of rotorcraft, and while current numerical analysis tools can, in theory, model the complete flow field, in practice the accuracy of these tools is limited by various inherent numerical deficiencies. An approach that combines the first-principles physical modeling capability of CFD schemes with the vortex preservation capabilities of Lagrangian vortex methods has been developed recently that controls the numerical diffusion of the rotor wake in a grid-based solver by employing a vorticity-velocity, rather than primitive variable, formulation. Coupling strategies, including variable exchange protocols are evaluated using several unstructured, structured, and Cartesian-grid Reynolds Averaged Navier-Stokes (RANS)/Euler CFD solvers. Results obtained with the hybrid grid-based solvers illustrate the capability of this hybrid method to resolve vortex-dominated flow fields with lower cell counts than pure RANS/Euler methods

Hybrid finite difference/finite element immersed boundary method

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach employs a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach

Pulsing corals: A story of scale and mixing

Effective methods of fluid transport vary across scale. A commonly used dimensionless number for quantifying the effective scale of fluid transport is the Reynolds number, Re, which gives the ratio of inertial to viscous forces. What may work well for one Re regime may not produce significant flows for another. These differences in scale have implications for many organisms, ranging from the mechanics of how organisms move through their fluid environment to how hearts pump at various stages in development. Some organisms, such as soft pulsing corals, actively contract their tentacles to generate mixing currents that enhance photosynthesis. Their unique morphology and intermediate scale where both viscous and inertial forces are significant make them a unique model organism for understanding fluid mixing. In this paper, 3D fluid-structure interaction simulations of a pulsing soft coral are used to quantify fluid transport and fluid mixing across a wide range of Re. The results show that net transport is negligible for $Re<10$, and continuous upward flow is produced for $Re\geq 10$.Comment: 8 pages, 8 figure

Analysis and discretization of the volume penalized Laplace operator with Neumann boundary conditions

We study the properties of an approximation of the Laplace operator with Neumann boundary conditions using volume penalization. For the one-dimensional Poisson equation we compute explicitly the exact solution of the penalized equation and quantify the penalization error. Numerical simulations using finite differences allow then to assess the discretisation and penalization errors. The eigenvalue problem of the penalized Laplace operator with Neumann boundary conditions is also studied. As examples in two space dimensions, we consider a Poisson equation with Neumann boundary conditions in rectangular and circular domains

Three Dimensional Pseudo-Spectral Compressible Magnetohydrodynamic GPU Code for Astrophysical Plasma Simulation

This paper presents the benchmarking and scaling studies of a GPU accelerated three dimensional compressible magnetohydrodynamic code. The code is developed keeping an eye to explain the large and intermediate scale magnetic field generation is cosmos as well as in nuclear fusion reactors in the light of the theory given by Eugene Newman Parker. The spatial derivatives of the code are pseudo-spectral method based and the time solvers are explicit. GPU acceleration is achieved with minimal code changes through OpenACC parallelization and use of NVIDIA CUDA Fast Fourier Transform library (cuFFT). NVIDIAs unified memory is leveraged to enable over-subscription of the GPU device memory for seamless out-of-core processing of large grids. Our experimental results indicate that the GPU accelerated code is able to achieve upto two orders of magnitude speedup over a corresponding OpenMP parallel, FFTW library based code, on a NVIDIA Tesla P100 GPU. For large grids that require out-of-core processing on the GPU, we see a 7x speedup over the OpenMP, FFTW based code, on the Tesla P100 GPU. We also present performance analysis of the GPU accelerated code on different GPU architectures - Kepler, Pascal and Volta