A low-numerical dissipation, patch-based adaptive-mesh-refinement method for large-eddy simulation of compressible flows

This paper describes a hybrid finite-difference method for the large-eddy simulation of compressible flows with low-numerical dissipation and structured adaptive mesh refinement (SAMR). A conservative flux-based approach is described with an explicit centered scheme used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. Three-dimensional numerical simulations of a Richtmyer-Meshkov instability are presented

A Lattice Boltzmann method in generalized curvilinear coordinat

A second-order central time-explicit method is implemented to solve the Lattice Boltzmann Equation in generalized curvilinear coordinates in order to simulate fluid flows with non-uniform grids and curved boundaries. Several test cases are used for verification, including the Taylor-Green vortex in two-dimensions, the square lid-driven cavity and the 2D circular cylinder. The Taylor-Green vortex is a classical benchmark test that is compared with the analytical solution using a non-uniform grid. The 2D lid-driven cavity is solved for moderate Reynolds numbers, where a clustering function is employed to stretch the mesh and increase the resolution in the cavity corners. The boundary conditions for these two test-cases are relatively straightforward to implement since there are no curved walls. Therefore, the 2D circular cylinder is used to demonstrate the capacity of the present method to perform steady and unsteady simulations with curved boundaries. Our results have been compared with the literature available, and the outcomes of this method are consistent with other results, confirming the feasibility of the implemented scheme. In addition, the present method has been compared to our own standard Cartesian lattice Boltzmann solver with adaptive mesh refinement for the 2D circular cylinder problem

Dynamical separation of spherical bodies in supersonic flow

An experimental and computational investigation of the unsteady separation behaviour of two spheres in Mach-4 flow is carried out. The spherical bodies, initially contiguous, are released with negligible relative velocity and thereafter fly freely according to the aerodynamic forces experienced. In experiments performed in a supersonic Ludwieg tube, nylon spheres are initially suspended in the test section by weak threads which are detached by the arrival of the flow. The subsequent sphere motions and unsteady flow structures are recorded using high-speed (13 kHz) focused shadowgraphy. The qualitative separation behaviour and the final lateral velocity of the smaller sphere are found to vary strongly with both the radius ratio and the initial alignment angle of the two spheres. More disparate radii and initial configurations in which the smaller sphere centre lies downstream of the larger sphere centre each increases the tendency for the smaller sphere to be entrained within the flow region bounded by the bow shock of the larger body, rather than expelled from this region. At a critical angle for a given radius ratio (or a critical radius ratio for a given angle), transition from entrainment to expulsion occurs; at this critical value, the final lateral velocity is close to maximum due to the same ‘surfing’ effect noted by Laurence & Deiterding (J. Fluid Mech., vol. 676, 2011, pp. 396–431) at hypersonic Mach numbers. A visualization-based tracking algorithm is used to provide quantitative comparisons between the experiments and high-resolution inviscid numerical simulations, with generally favourable agreement

Hydrodynamic instabilities in gaseous detonations: comparison of Euler, Navier–Stokes, and large-eddy simulation

A large-eddy simulation is conducted to investigate the transient structure of an unstable detonation wave in two dimensions and the evolution of intrinsic hydrodynamic instabilities. The dependency of the detonation structure on the grid resolution is investigated, and the structures obtained by large-eddy simulation are compared with the predictions from solving the Euler and Navier–Stokes equations directly. The results indicate that to predict irregular detonation structures in agreement with experimental observations the vorticity generation and dissipation in small scale structures should be taken into account. Thus, large-eddy simulation with high grid resolution is required. In a low grid resolution scenario, in which numerical diffusion dominates, the structures obtained by solving the Euler or Navier–Stokes equations and large-eddy simulation are qualitatively similar. When high grid resolution is employed, the detonation structures obtained by solving the Euler or Navier–Stokes equations directly are roughly similar yet equally in disagreement with the experimental results. For high grid resolution, only the large-eddy simulation predicts detonation substructures correctly, a fact that is attributed to the increased dissipation provided by the subgrid scale model. Specific to the investigated configuration, major differences are observed in the occurrence of unreacted gas pockets in the high-resolution Euler and Navier–Stokes computations, which appear to be fully combusted when large-eddy simulation is employed

Parallel Eulerian-Lagrangian Method with Adaptive Mesh Refinement for Moving Boundary Computation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106477/1/AIAA2013-370.pd

An open and parallel multiresolution framework using block-based adaptive grids

A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and explicit time integration. Grid refinement and coarsening are triggered by multiresolution analysis, i.e. thresholding of wavelet coefficients, which allow controlling the precision of the adaptive approximation of the solution with respect to uniform grid computations. The implementation of the scheme is fully parallel using MPI with a hybrid data structure. Load balancing relies on space filling curves techniques. Validation tests for 2D advection equations allow to assess the precision and performance of the developed code. Computations of the compressible Navier-Stokes equations for a temporally developing 2D mixing layer illustrate the properties of the code for nonlinear multi-scale problems. The code is open source