Moving Overlapping Grids with Adaptive Mesh Refinement for High-Speed Reactive and Non-reactive Flow

We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in the flow such as shocks and detonations. Refinement grids are added to base-level grids according to an estimate of the error, and these refinement grids move with their corresponding base-level grids. The numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from (fixed) parameter space to (moving) physical space. The mapped equations are solved numerically using a second-order extension of Godunov's method. The stiff source term in the reactive case is handled using a Runge-Kutta error-control scheme. We consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid. In the latter case, the Newton-Euler equations describe the motion of the center of mass of the each body and the rotation about it, and these equations are integrated numerically using a second-order predictor-corrector scheme. Numerical boundary conditions at slip walls are described, and numerical results are presented for both reactive and non-reactive flows in order to demonstrate the use and accuracy of the numerical approach

A Nitsche-based cut finite element method for a fluid--structure interaction problem

We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The coupling between the embedded and background fluid meshes is enforced using a stabilized Nitsche formulation which allows us to establish stability and optimal order \emph{a priori} error estimates, see~\cite{MassingLarsonLoggEtAl2013}. We consider here a steady state fluid--structure interaction problem where a hyperelastic structure interacts with a viscous fluid modeled by the Stokes equations. We evaluate an iterative solution procedure based on splitting and present three-dimensional numerical examples.Comment: Revised version, 18 pages, 7 figures. Accepted for publication in CAMCo

A stable FSI algorithm for light rigid bodies in compressible flow

In this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid-structure interactions of light rigid bodies and inviscid compressible flow. The new algorithm is stable even for bodies with zero mass and zero moments of inertia. The approach is based on a local characteristic projection of the force on the rigid body and is a natural extension of the recently developed algorithm for coupling compressible flow and deformable bodies. Normal mode analysis is used to prove the stability of the approximation for a one-dimensional model problem and numerical computations confirm these results. In multiple space dimensions the approach naturally reveals the form of the added mass tensors in the equations governing the motion of the rigid body. These tensors, which depend on certain surface integrals of the fluid impedance, couple the translational and angular velocities of the body. Numerical results in two space dimensions, based on the use of moving overlapping grids and adaptive mesh refinement, demonstrate the behavior and efficacy of the new scheme. These results include the simulation of the difficult problem of a shock impacting an ellipse of zero mass.Comment: 32 pages, 20 figure

Numerical simulation of the aerodynamic performance of an H-rotor.

Vertical axis wind turbines (VAWTs) are devices to convert wind energy into electricity. Unlike horizontal axis wind turbines (HAWT) where the main rotor shaft is set horizontally, VAWTs use vertical rotor shaft. Unlike HAWTs, VAWTs can be effectively used in urban environment where flow is characterized with unsteadiness and turbulence. The efficiency of the VA WTs highly depends on the aerodynamics of the wind blades. In this thesis we study the aerodynamics of the H-rotor, one type of VAWTs using computational fluid dynamics methods. Two different approaches are used in this study. One is based on direct numerical simulation (DNS) method and another is based on Reynolds averaged Navier-Stoke (RANS) model. For DNS study we solve the incompressible Navier-Stokes equations with a CFD package, OVERTURE. An overlapping moving grids technique is employed to handle the rotation of the wind turbine. For RANS simulation we used a commercial CFD package ANSYS-Fluent. The sliding mesh model of ANSYS-Fluent is applied to evaluate unsteady interaction between the stationary and rotating components. Our simulation shows that the DNS cannot correctly predict the power coefficient due to the lack of grid resolution at high Reynolds numbers. The RANS simulation results closely match the experimental data and RANS provides a way to study wind turbine aerodynamics in an efficient and reliable manner. Our simulation shows that the rotor with NACA0015 blade section obtains a maximum power coefficient of 0.16 at tip speed ratio of 2.5 for mean wind velocity of 3.9m/s. By replacing the blade section with NACA0022 airfoil profile, the maximum power coefficient of the rotor can be improved to 0.21 at tip speed ratio of 2.5 in the same wind conditions

Implicit High-Order Flux Reconstruction Solver for High-Speed Compressible Flows

The present paper addresses the development and implementation of the first high-order Flux Reconstruction (FR) solver for high-speed flows within the open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid Dynamics) platform. The resulting solver is fully implicit and able to simulate compressible flow problems governed by either the Euler or the Navier-Stokes equations in two and three dimensions. Furthermore, it can run in parallel on multiple CPU-cores and is designed to handle unstructured grids consisting of both straight and curved edged quadrilateral or hexahedral elements. While most of the implementation relies on state-of-the-art FR algorithms, an improved and more case-independent shock capturing scheme has been developed in order to tackle the first viscous hypersonic simulations using the FR method. Extensive verification of the FR solver has been performed through the use of reproducible benchmark test cases with flow speeds ranging from subsonic to hypersonic, up to Mach 17.6. The obtained results have been favorably compared to those available in literature. Furthermore, so-called super-accuracy is retrieved for certain cases when solving the Euler equations. The strengths of the FR solver in terms of computational accuracy per degree of freedom are also illustrated. Finally, the influence of the characterizing parameters of the FR method as well as the the influence of the novel shock capturing scheme on the accuracy of the developed solver is discussed