Differential formulation of discontinuous Galerkin and related methods for compressible Euler and Navier-Stokes equations

A new approach to high-order accuracy for the numerical solution of conservation laws introduced by Huynh and extended to simplexes by the current work is renamed CPR (correction procedure or collocation penalty via reconstruction). The CPR approach employs the differential form of the equation and accounts for the jumps in flux values at the cell boundaries by a correction procedure. In addition to being simple and economical, it unifies several existing methods including discontinuous Galerkin (DG), staggered grid, spectral volume (SV), and spectral difference (SD). The approach is then extended to diffusion equation and Navier-Stokes equations. In the discretization of the diffusion terms, the BR2 (Bassi and Rebay), interior penalty, compact DG (CDG), and I-continuous approaches are used. The first three of these approaches, originally derived using the integral formulation, were recast here in the CPR framework, whereas the I-continuous scheme, originally derived for a quadrilateral mesh, was extended to a triangular mesh. The current work also includes a study of high-order curve boundaries representations. A new boundary representation based on the Bezier curve is then developed and analyzed, which is shown to have several advantages for complicated geometries. To further enhance the efficiency, the capability of h/p mesh adaptation is developed for the CPR solver. The adaptation is driven by an efficient multi-p a posteriori error estimator. P-adaptation is applied to smooth regions of the flow field while h-adaptation targets the non-smooth regions, identified by accuracy-preserving TVD marker. Several numerical tests are presented to demonstrate the capability of the technique

A computational study of quasi-2D flows at low Reynolds numbers

Previous studies on low Reynolds number quasi-2D flow around airfoils were mostly two-dimensional, with issues for stalling behavior at higher angles of attack (AOAs). In the present work, a computational study was conducted to investigate the unsteady quasi-2D flow around a streamlined NASA low-speed GA(W)-1 airfoil and a corrugated dragonfly airfoil at the Reynolds numbers of 68,000 and 55,000 with both 2D and 3D simulations. These simulations were carried out by solving the unsteady 2D and 3D Navier-Stokes equations to predict the behavior of the unsteady flow structures around the airfoils at different AOAs. Extensive comparisons were made between the numerical results and wind-tunnel experimental results for the same configurations. It was found that the 2D and 3D simulations differ significantly at relatively high AOAs, and that the 3D computational results agree much better with the experimental data. It is believed that unsteady vortex-dominated flow at high angle of attack is strongly three-dimensional. As a result, the 2D simulations are not adequate in resolving the fundamental flow physics, and 3D simulations are necessary to correctly predict the flow behavior at such conditions

Numerical Simulation of Unsteady Flow in a Scroll Compressor

Scroll compressors are widely used in many industries. It is considered that scroll compressors have the advantage of high efficiency, lower noise and vibration levels. There are various losses in a scroll compressor that need to be studied to achieve better efficiency, of which the most significant is the flow losses, especially the losses at discharge. Computational fluid dynamics (CFD) simulations can be a useful tool in understanding the flow field and help reduce the flow losses through design optimizations. There are few numerical studies on the flow inside the scroll compressor. The reason is that defining the mesh and its movement in the scroll rotor can be demanding. The flow field of a scroll compressor is unsteady and 3-dimensional, consisting of gas pockets with changing geometry and volume. More often than not, check valves are used at the discharge to prevent reverse flow, which complicates the setup of the numerical simulation. The present work demonstrates a newly developed rotor template tool for scroll compressors/ expanders. This scroll template generates high-quality structure mesh from the outlines of stationary and orbiting rotors, which are input from the user. The mesh movement is also automatically calculated to account for every position of the orbiting rotor, maintaining good grid quality and smooth movement through the whole revolution. The tool greatly simplifies the setup of the CFD simulation and can significantly reduce turn-around time. Moreover, the check valve is simulated with the flip valve template tool. Here, the bending deformation of the flexible reed valve plate is replaced by a rigid body rotation. With judicious choices of torsional elastic constant and preload torque, the valve opening at the center of the discharging port can be setup to mimic that of a flexible flap. The rotor and valve components are then combined, to provide a complete solution for scroll compressor/ expander flow simulations

Deformable Groupwise Registration Using a Locally Low-Rank Dissimilarity Metric for Myocardial Strain Estimation from Cardiac Cine MRI Images

Objective: Cardiovascular magnetic resonance-feature tracking (CMR-FT) represents a group of methods for myocardial strain estimation from cardiac cine MRI images. Established CMR-FT methods are mainly based on optical flow or pairwise registration. However, these methods suffer from either inaccurate estimation of large motion or drift effect caused by accumulative tracking errors. In this work, we propose a deformable groupwise registration method using a locally low-rank (LLR) dissimilarity metric for CMR-FT. Methods: The proposed method (Groupwise-LLR) tracks the feature points by a groupwise registration-based two-step strategy. Unlike the globally low-rank (GLR) dissimilarity metric, the proposed LLR metric imposes low-rankness on local image patches rather than the whole image. We quantitatively compared Groupwise-LLR with the Farneback optical flow, a pairwise registration method, and a GLR-based groupwise registration method on simulated and in vivo datasets. Results: Results from the simulated dataset showed that Groupwise-LLR achieved more accurate tracking and strain estimation compared with the other methods. Results from the in vivo dataset showed that Groupwise-LLR achieved more accurate tracking and elimination of the drift effect in late-diastole. Inter-observer reproducibility of strain estimates was similar between all studied methods. Conclusion: The proposed method estimates myocardial strains more accurately due to the application of a groupwise registration-based tracking strategy and an LLR-based dissimilarity metric. Significance: The proposed CMR-FT method may facilitate more accurate estimation of myocardial strains, especially in diastole, for clinical assessments of cardiac dysfunction