Three-dimensional building-cube method for inviscid compressible flow computations

A high-order accurate unstructured spectral difference lattice Boltzmann method for computing inviscid and viscous compressible flows

SummaryProper orthogonal decomposition (POD) allows to compress information by identifying the most energetic modes obtained from a database of snapshots. In this work, POD is used to predict the behavior of compressible flows by means of global and local approaches, which exploit some features of a discontinuous Galerkin spatial discretization. The presented global approach requires the definition of high‐order and low‐order POD bases, which are built from a database of high‐fidelity simulations. Predictions are obtained by performing a cheap low‐order simulation whose solution is projected on the low‐order basis. The projection coefficients are then used for the reconstruction with the high‐order basis. However, the nonlinear behavior related to the advection term of the governing equations makes the use of global POD bases quite problematic. For this reason, a second approach is presented in which an empirical POD basis is defined in each element of the mesh. This local approach is more intrusive with respect to the global approach but it is able to capture better the nonlinearities related to advection. The two approaches are tested and compared on the inviscid compressible flow around a gas‐turbine cascade and on the compressible turbulent flow around a wind turbine airfoil.

A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer–Nunziato model

This paper details a multigrid‐accelerated cut‐cell non‐conforming Cartesian mesh methodology for the modelling of inviscid compressible and incompressible flow. This is done via a single equation set that describes sub‐, trans‐, and supersonic flows. Cut‐cell technology is developed to furnish body‐fitted meshes with an overlapping mesh as starting point, and in a manner which is insensitive to surface definition inconsistencies. Spatial discretization is effected via an edge‐based vertex‐centred finite volume method. An alternative dual‐mesh construction strategy, similar to the cell‐centred method, is developed. Incompressibility is dealt with via an artificial compressibility algorithm, and stabilization achieved with artificial dissipation. In compressible flow, shocks are captured via pressure switch‐activated upwinding. The solution process is accelerated with full approximation storage (FAS) multigrid where coarse meshes are generated automatically via a volume agglomeration methodology. This is the first time that the proposed discretization and solution methods are employed to solve a single compressible–incompressible equation set on cut‐cell Cartesian meshes. The developed technology is validated by numerical experiments. The standard discretization and alternative methods were found equivalent in accuracy and computational cost. The multigrid implementation achieved decreases in CPU time of up to one order of magnitude. Copyright © 2007 John Wiley & Sons, Ltd.

The near term availability of scientific supercomputers will soon permit routine simulation of three dimensional compressible flow about relatively complex configurations.KeywordsAIAA PaperThree Dimensional FlowUpwind SchemeRefined GridTransonic FlowThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Convergence of cognitive and adaptive decline in chronic schizophrenia

ABSTRACTIn the present study, a high‐order hybrid compact‐weighted essentially non‐oscillatory (WENO) scheme is applied in conjunction with the immersed boundary method for efficiently computing compressible inviscid flows around two‐dimensional solid bodies. For this aim, the two‐dimensional unsteady compressible Euler equations written in the conservative form are considered and they are discretized in the space by using the hybrid fifth‐order compact‐WENO (CW) finite‐difference scheme and the third‐order explicit TVD Runge–Kutta scheme in the time. The solid bodies are appropriately imposed to the computational domain by using the immersed boundary method as an effective procedure in modeling the complex configurations without the difficulties usually encountered in generating the computational grid over such problems. Different test cases are simulated by applying the hybrid CW immersed boundary method and the present results are compared with those of available finite‐difference immersed boundary methods. To further assess the solution method applied, the present results are also obtained by the high‐order WENO immersed boundary scheme, and these two high‐order accurate solution procedures are thoroughly compared with each other. The main advantage of using the hybrid CW finite‐difference immersed boundary method applied here is that it provides a more accurate solution with lower computational cost in comparison with the traditional and high‐order WENO finite‐difference immersed boundary methods. It is shown that the solution procedure based on the hybrid CW scheme implemented via the immersed boundary method has still reasonable shock‐capturing features and it can effectively be applied for accurately computing the compressible inviscid flows with the complicated flow structures and the embedded discontinuities such as the shocks over the complicated geometries.

Numerical simulation of multi-dimensional inviscid compressible flows by using TV-HLL scheme

Non-reflective boundary conditions are essential for many numerical flow simulations, especially when sound waves are present. This is the case for the numerical simulation of subsonic compressible flows in interior domains with moving boundaries, where the movement of the boundary will generate soundwaves. When such a flow is simulated numerically, usual boundary conditions at the in- and outflow boundary reflect the generated sound waves and cause the simulation to quickly break down. We have derived non-reflective boundary conditions for subsonic, viscous, compressible flows. In order to restrict the computational and formal effort, we only consider the two-dimensional case, the extension to three dimensions is straightforward.

Features of the simulation of low-velocity inviscid and viscous compressible gas flows are considered, and a finite-volume discretization of gas dynamics equations at low Mach numbers on unstructured meshes is discussed. Preconditioning based on the use of physical variables is used to speed up the convergence of time marching to a steady state and to improve the accuracy of the steady-state solution. The structure of the preconditioning matrix and the diagonalization of the Jacobian of the preconditioned system of equations are discussed. The capabilities of this approach are demonstrated using model gasdynamic simulations ing a wide range of Mach numbers.

Shock waves interacting with multi-material interfaces in compressible flows result in complex shock diffraction patterns involving total or partial reflection, refraction and transmission of the impinging shock wave. To simulate such complicated interfacial dynamics problems, a fixed Cartesian grid approach in conjunction with level set interface tracking is attractive. In this regard, a unified Riemann solver based Ghost Fluid Method (GFM) was developed to accurately resolve and represent the embedded solid and fluid object(s) in high speed compressible multiphase flows. While the GFM-based Cartesian grid approach significantly alleviates the complexity associated with mesh management, the method lacks flexibility in effective grid point placement in regions with rich structures in the flow field. Thus for higher-order and highly accurate sharp interface Cartesian grid based calculations with optimal computational effort, it is imperative to supplement the solution with adaptive mesh refinement technique. Hence in this work, a simple procedure is presented to complement the Riemann solver based GFM approach with quadtree (octree in three dimensions) based Local Mesh Refinement (LMR) technique for efficient and high fidelity computations involving strong shock interactions in multiphase compressible flows. The paper reports on a simple, conservative formulation for accurate calculation of ENO-based numerical fluxes at the fine-coarse mesh boundary. The numerical examples displayed in this paper clearly demonstrate that the methodology is consistent in generating satisfactory solutions, and effectively capturing fine structures in the flow.

Attempts to simulate compressible flows with moderate Mach number to relatively high ones using Lattice Boltzmann Method (LBM) have been made by numerous researchers in the recent decade. The stability of the LBM is a challenging problem in the simulation of compressible flows with different types of embedded discontinuities. The present study proposes an approach for simulation of inviscid flows by a compressible LB model in order to enhance the robustness using a combination of Essentially NonOscillatory (ENO) scheme and Shock-Detecting Sensor (SDS) procedure. A sensor is introduced with adjustable parameters which is active near the discontinuities and affects less on smooth regions. The validity of the improved model to capture shocks and to resolve contact discontinuity and rarefaction waves in the well-known benchmarks such as, Riemann problem, and shock reflection is investigated. In addition, the problem of supersonic flow in a channel with ramp is simulated using a skewed rectangular grid generated by an algebraic grid generation method. The numerical results are compared with analytical ones and those obtained by solving the original model. The numerical results show that the presented scheme is capable of generating more robust solutions in the simulation of compressible flows and is almost free of oscillations for high Mach numbers. Good agreements are obtained for all problems.

A simple distribution function-based gas-kinetic scheme for simulation of viscous incompressible and compressible flows

A multichannel code distribution protocol for remote reprogramming in WSNs

An explicit determination of all local conservation laws of kinematic type on moving domains and moving surfaces is presented for the Euler equations of inviscid compressible fluid flow in curved Riemannian manifolds in n >1 dimensions. All corresponding kinematic constants of motion are also determined, along with all Hamiltonian kinematic symmetries and kinematic Casimirs which arise from the Hamiltonian structure of the inviscid compressible fluid equations.