Augmented Stabilized and Galerkin Least Squares Formulations

Ranjan, Rakesh; Feng, Yusheng; Chronopolous, Anthony Theodore

doi:10.5539/jmr.v8n6p1

Cited by 5 publications

(2 citation statements)

References 33 publications

(48 reference statements)

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“…One of them is the Galerkin Least Squares (GLS) stabilization method. GLS is a general stabilization method applicable to a wide range of problems 35 – 39 . Its theoretical basis is that the test function should be chosen so as to minimize the squared residual of the equations.…”

Section: Two-fluid Turbulence Modelmentioning

confidence: 99%

Validation of a two-fluid turbulence model in comsol multiphysics for the problem of flow around aerodynamic profiles

Malikov,

Madaliev,

Chernyshev

et al. 2024

Sci Rep

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The article presents a study of a two-fluid turbulence model in the Comsol Multiphysics software package for the problem of a subsonic flow around the DSMA661 and NACA 4412 airfoils with angles of attack of 0 and 13.87 degrees, respectively. In this paper, the finite element method is used for the numerical implementation of the turbulence equations. To stabilize the discretized equations, stabilization by the Galerkin least squares method was used. The results obtained are compared with the results of other RANS, LES, DES models and experimental data. It is shown that in the case of continuous flow around the DSMA661 airfoil, the results of the two-fluid model are very close to the SST results and are in good agreement with the experimental data. When flowing around the NACA 4412 airfoil, flow separation occurs and a recirculation zone appears. It is shown that in such cases the two-fluid model gives more accurate results than other turbulence models. Implementation of the Comsol Multiphysics software package showed good convergence, stability, and high accuracy of the two-fluid turbulence model.

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Section: Two-fluid Turbulence Modelmentioning

confidence: 99%

Validation of a two-fluid turbulence model in comsol multiphysics for the problem of flow around aerodynamic profiles

Malikov,

Madaliev,

Chernyshev

et al. 2024

Sci Rep

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“…Finite element methods, in general, (1) are more amenable to complex discretizations and unstructured meshes, (2) do not require an interstencil construction of high-order approximations, (3) are not locally lower order near the limiters as are high-order finite volume schemes, and (4) have well-defined boundary conditions, not dependent on local metrics to transform the fluxes on the provided faces in a high-order context. Augmentation of incompressible flow formulation ASUPG and AGLS was first presented in a technical report by Ranjan [6] and formally in a paper by Ranjan et al [7,8]. If one were to compare finite volume, spectral element methods, and finite element-based schemes, the coarse element counts that finite volume methods require provide a high competitive edge versus extensive refinements are required by low-order finite element methods.…”

Section: Introductionmentioning

confidence: 99%

A Spectral/hp-Based Stabilized Solver with Emphasis on the Euler Equations

Ranjan,

Catabriga,

Araya

2024

Fluids

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The solution of compressible flow equations is of interest with many aerospace engineering applications. Past literature has focused primarily on the solution of Computational Fluid Dynamics (CFD) problems with low-order finite element and finite volume methods. High-order methods are more the norm nowadays, in both a finite element and a finite volume setting. In this paper, inviscid compressible flow of an ideal gas is solved with high-order spectral/hp stabilized formulations using uniform high-order spectral element methods. The Euler equations are solved with high-order spectral element methods. Traditional definitions of stabilization parameters used in conjunction with traditional low-order bilinear Lagrange-based polynomials provide diffused results when applied to the high-order context. Thus, a revision of the definitions of the stabilization parameters was needed in a high-order spectral/hp framework. We introduce revised stabilization parameters, τsupg, with low-order finite element solutions. We also reexamine two standard definitions of the shock-capturing parameter, δ: the first is described with entropy variables, and the other is the YZβ parameter. We focus on applications with the above introduced stabilization parameters and analyze an array of problems in the high-speed flow regime. We demonstrate spectral convergence for the Kovasznay flow problem in both L1 and L2 norms. We numerically validate the revised definitions of the stabilization parameter with Sod’s shock and the oblique shock problems and compare the solutions with the exact solutions available in the literature. The high-order formulation is further extended to solve shock reflection and two-dimensional explosion problems. Following, we solve flow past a two-dimensional step at a Mach number of 3.0 and numerically validate the shock standoff distance with results obtained from NASA Overflow 2.2 code. Compressible flow computations with high-order spectral methods are found to perform satisfactorily for this supersonic inflow problem configuration. We extend the formulation to solve the implosion problem. Furthermore, we test the stabilization parameters on a complex flow configuration of AS-202 capsule analyzing the flight envelope. The proposed stabilization parameters have shown robustness, providing excellent results for both simple and complex geometries.

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