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Zeng, Xianyang; Xiao, Min; Ni, Guoxi
doi: 10.1002/fld.4233pmid: N/A
This paper presents an efficient method to simulate the reactive flow for general equation of states with the compressible fluid model coupled with reactive rate equation. The important aspect is to deal with mixture of different phases in one cell, which will inevitably happen in the Eulerian method for reactive flow. Physical variables such as the pressure,velocity, and speed of sound in each cell need to be reconstructed for the Harten‐Lax‐Leer‐Contact (HLLC) Riemann solver, which will result in nonlinear algebra equations, and these reconstructed variables are used to obtain the flux. Numerical examples of stable and unstable detonations with different equation of states demonstrate the accuracy and efficiency of this method. Copyright © 2016 John Wiley & Sons, Ltd.
Mifsud, M. J.; MacManus, D. G.; Shaw, S.T.
doi: 10.1002/fld.4234pmid: N/A
A variable‐fidelity aerodynamic model based on proper orthogonal decomposition (POD) of an ensemble of computational fluid dynamics (CFD) solutions at different parameters is presented in this article. The ensemble of CFD solutions consists of two subsets of numerical solutions or snapshots computed at two different nominal orders of accuracy or discretization. These two subsets are referred to as the low‐fidelity and high‐fidelity solutions or data, whereby the low fidelity corresponds with computations made at the lower nominal order of accuracy or coarser discretization. In this model, the relatively inexpensive low‐fidelity data and the more accurate but expensive high‐fidelity data are considered altogether to devise an efficient prediction methodology involving as few high‐fidelity analyses as possible, while obtaining the desired level of detail and accuracy. The POD of this set of variable‐fidelity data produces an optimal linear set of orthogonal basis vectors that best describe the ensemble of numerical solutions altogether. These solutions are projected onto this set of basis vectors to provide a finite set of scalar coefficients that represent either the low‐fidelity or high‐fidelity solutions. Subsequently, a global response surface is constructed through this set of projection coefficients for each basis vector, which allows predictions to be made at parameter combinations not in the original set of observations. This approach is used to predict supersonic flow over a slender configuration using Navier–Stokes solutions that are computed at two different levels of nominal accuracy as the low‐fidelity and high‐fidelity solutions. The numerical examples show that the proposed model is efficient and sufficiently accurate. Copyright © 2016 John Wiley & Sons, Ltd.
Gao, X.; Owen, L. D.; Guzik, S. M. J.
doi: 10.1002/fld.4235pmid: N/A
A fourth‐order finite‐volume method for solving the Navier–Stokes equations on a mapped grid with adaptive mesh refinement is proposed, implemented, and demonstrated for the prediction of unsteady compressible viscous flows. The method employs fourth‐order quadrature rules for evaluating face‐averaged fluxes. Our approach is freestream preserving, guaranteed by the way of computing the averages of the metric terms on the faces of cells. The standard Runge–Kutta marching method is used for time discretization. Solutions of a smooth flow are obtained in order to verify that the method is formally fourth‐order accurate when applying the nonlinear viscous operators on mapped grids. Solutions of a shock tube problem are obtained to demonstrate the effectiveness of adaptive mesh refinement in resolving discontinuities. A Mach reflection problem is solved to demonstrate the mapped algorithm on a non‐rectangular physical domain. The simulation is compared against experimental results. Future work will consider mapped multiblock grids for practical engineering geometries. Copyright © 2016 John Wiley & Sons, Ltd.
Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.; Tomov, V. Z.
doi: 10.1002/fld.4236pmid: N/A
We present a new closure model for single fluid, multi‐material Lagrangian hydrodynamics and its application to high‐order finite element discretizations of these equations . The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high‐order variational generalization of the method of Tipton . This computation is defined by the notion of partial non‐instantaneous pressure equilibration, while the full pressure equilibration is achieved by both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one‐dimensional two‐material problems, followed by two‐dimensional and three‐dimensional multi‐material high‐velocity impact arbitrary Lagrangian–Eulerian calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.
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