A sharp interface Cartesian grid method for viscous simulation of shocked particle-laden flows

A Cartesian grid-based sharp interface method is presented for viscous simulations of shocked particle-laden flows. The moving solid–fluid interfaces are represented using level sets. A moving least-squares reconstruction is developed to apply the no-slip boundary condition at solid–fluid interfaces and to supply viscous stresses to the fluid. The algorithms developed in this paper are benchmarked against similarity solutions for the boundary layer over a fixed flat plate and against numerical solutions for moving interface problems such as shock-induced lift-off of a cylinder in a channel. The framework is extended to 3D and applied to calculate low Reynolds number steady supersonic flow over a sphere. Viscous simulation of the interaction of a particle cloud with an incident planar shock is demonstrated; the average drag on the particles and the vorticity field in the cloud are compared to the inviscid case to elucidate the effects of viscosity on momentum transfer between the particle and fluid phases. The methods developed will be useful for obtaining accurate momentum and heat transfer closure models for macro-scale shocked particulate flow applications such as blast waves and dust explosions.     

A sharp interface method for high-speed multi-material flows: strong shocks and arbitrary materialpairs

A general framework is developed for solving high-speed and high-intensity multi-material interaction problems on adaptively refined Cartesian meshes. The framework is applicable for interfaces separating materials with very different properties and in the presence of strong shocks. A sharp interface treatment is maintained through a modified Ghost Fluid Method. The embedded boundaries are tracked and represented with level sets. A tree-based Local Mesh Refinement scheme is employed to efficiently resolve the desired physics. Results are shown for situations that cover varied combination of materials (fluids, rigid solids and deformable solids) with careful benchmarking to establish the validity and the versatility of the approach.     

A discontinuous Galerkin immersed boundary solver for compressible flows: Adaptive local time stepping for artificial viscosity–based shock-capturing on cut cells

We present a higher-order cut cell immersed boundary method (IBM) for the simulation of high Mach number flows. As a novelty on a cut cell grid, we evaluate an adaptive local time stepping (LTS) scheme in combination with an artificial viscosity–based shock-capturing approach. The cut cell grid is optimized by a nonintrusive cell agglomeration strategy in order to avoid problems with small or ill-shaped cut cells. Our approach is based on a discontinuous Galerkin discretization of the compressible Euler equations, where the immersed boundary is implicitly defined by the zero isocontour of a level set function. In flow configurations with high Mach numbers, a numerical shock-capturing mechanism is crucial in order to prevent unphysical oscillations of the polynomial approximation in the vicinity of shocks. We achieve this by means of a viscous smoothing where the artificial viscosity follows from a modal decay sensor that has been adapted to the IBM. The problem of the severe time step restriction caused by the additional second-order diffusive term and small nonagglomerated cut cells is addressed by using an adaptive LTS algorithm. The robustness, stability, and accuracy of our approach are verified for several common test cases. Moreover, the results show that our approach lowers the computational costs drastically, especially for unsteady IBM problems with complex geometries.     

A new immersed boundary method for compressible Navier–Stokes equations

This paper presents an immersed boundary method for compressible Navier–Stokes equations in irregular domains, based on a local radial basis function approximation. This approach allows one to define a reconstruction of the radial basis functions on each irregular interface cell to treat both the Dirichlet and Neumann boundary conditions accurately on the immersed interfaces. Several numerical examples, including problems with available analytical solutions and the well-documented flow past an airfoil, are presented to test the proposed method. The numerical results demonstrate that the proposed method provides accurate solutions for viscous compressible flows.     

Modelling far-field entrainment in compressible flows

A procedure that generates steady-states with accurate far-field entrainment is described here. It can be applied to any existing code originally designed for unsteady simulations. Such steady-states are obtained with physical-time damping, introduced through a dual time stepping methodology to effectively eliminate all transient fluctuations without affecting spatial resolution. Far-field entrainment is guaranteed by using properly selected local boundary conditions. Hence, reference profiles with accurate far-field entrainment are generated from the very same code that will eventually use them in unsteady simulations. This new procedure is tested on an unsteady code designed for compressible planar mixing-layer simulations at arbitrary Mach numbers. It is numerically stable for a wide range of Mach numbers and velocity ratios.     

可压流数值模拟中当地DFD方法的改进和应用

阐述了求解守恒型Euler 方程的当地DFD (Domain-Free Discretization) 方法的改进和应用。DFD 离散策略的核心,是解域内点上控制方程的离散形式可与解域外的一些点相关。通过边界附近解的近似形式,外部相关点上的流动变量值得到确定并强加相应的边界条件。与最初的当地DFD方法不同,在解的近似形式构建中,采用了CCST技术 (Curvature-Corrected Symmetry Technique),因此外部相关点上的密度和切向速度分别由等熵和等总焓关系确定。空间离散采用Galerkin 有限体积格式。最后,给出了固定和运动物体可压缩绕流的数值模拟结果,以验证改进的当地DFD方法的可靠性和数值解精度的提高。     

触摸高温气体动力学

回顾了高温气体动力学与高超声速科技相关的一些重要研究进展,探讨几个具有基础性研究意义的方向：即高超声速流动模拟;高温气体热化学反应机制;高超声速流动滞止区预测;高超声速边界层转捩和激波/激波相互作用诱导的气动热问题．这些研究方向与高温气体效应和强激波密切相关,对高超声速科技关键技术的突破起着重要作用．