Verification and Scalability of Mixed-Element USM3D for Benchmark Three-Dimensional Flows

AIAA Journal ◽  
2021 ◽  
pp. 1-20
Author(s):  
Mohagna J. Pandya ◽  
Dennis C. Jespersen ◽  
Boris Diskin ◽  
James L. Thomas ◽  
Neal T. Frink
Keyword(s):  
Three Dimensional ◽  
Mixed Element

High Order Schemes on Three-Dimensional General Polyhedral Meshes — Application to the Level Set Method

2012 ◽  
Vol 12 (1) ◽  
pp. 1-41 ◽  
Author(s):  
Thibault Pringuey ◽  
R. Stewart Cant
Keyword(s):  
Level Set ◽  
Three Dimensional ◽  
Unstructured Meshes ◽  
High Order ◽  
Convex Polyhedra ◽  
Two Phase ◽  
High Order Schemes ◽  
Flow Problems ◽  
Mixed Element ◽  
Areas Of Interest

AbstractIn this article, we detail the methodology developed to construct arbitrarily high order schemes — linear and WENO — on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set.

Efficiency of Mixed-Element USM3D for Benchmark Three-Dimensional Flows

AIAA Journal ◽  
2021 ◽  
pp. 1-15
Author(s):  
Mohagna J. Pandya ◽  
Dennis C. Jespersen ◽  
Boris Diskin ◽  
James L. Thomas ◽  
Neal T. Frink
Keyword(s):  
Three Dimensional ◽  
Mixed Element

scholarly journals Finite Element Approximation and Numerical Analysis of Three-dimensional Electrical Impedance Tomography

2016 ◽  
Vol 8 (4) ◽  
pp. 99
Author(s):  
Yirang Yuan ◽  
Jiuping Li ◽  
Changfeng Li ◽  
Tongjun Sun
Keyword(s):  
Finite Element ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Three Dimensional ◽  
Invariance Property ◽  
Element Approximation ◽  
Computational Formula ◽  
Impedance Tomography ◽  
Mixed Element ◽  
Direct Problems

Electrical impedance tomography is solved by solving an inverse problem of elliptic equation, and a new numerical method or a new technique is argued to consider finite element (such as normal element and mixed element) in this paper on three dimensional region. Introducing different perturbations to boundary restrictions and using different spacial steps, the authors obtain numerical solutions and give comparison with exact solutions. Numerical data show that numerical solution can approximate exact solution well as spacial step taken small and the approximation of Neumann boundary condition is more stable than that of Dirichlet case.<br />For Newton iterations on finite element method, a large-scaled system of massive linear equations is solved in each iteration, thus the computation is quite expensive. So two techniques are argued in the first half of this paper. Firstly, the invariance property of quasi-element stiffness matrix is used in the  iterations and a type of special current model is introduced. Then the minimum number of direct problems solved is considered. Later a local conservative numerical approximation, low order mixed element (block-centered method) is presented in the latter part and the positive semi-definiteness and the existence of its solution are proved. Computational formula of error functional Jacobi matrix is derived and the least direct problems in each iteration are solved by using the symmetry of algorithm and a special current basis. This method has been applied successfully in actual numerical simulation of three-dimensional electrical impedance tomography.

Linearized Unsteady Viscous Turbomachinery Flows Using Hybrid Grids

2001 ◽  
Vol 123 (3) ◽  
pp. 568-582 ◽  
Author(s):  
L. Sbardella ◽  
M. Imregun
Keyword(s):  
Unsteady Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Laplacian Operator ◽  
Finite Volume Scheme ◽  
Test Case ◽  
Flow Equations ◽  
Mixed Element

The paper describes the theory and the numerical implementation of a three-dimensional finite volume scheme for the solution of the linearized, unsteady Favre-averaged Navier–Stokes equations for turbomachinery applications. A further feature is the use of mixed element grids, consisting of triangles and quadrilaterals in two dimensions, and of tetrahedra, triangular prisms, and hexahedra in three dimensions. The linearized unsteady viscous flow equations are derived by assuming small harmonic perturbations from a steady-state flow and the resulting equations are solved using a pseudo-time marching technique. Such an approach enables the same numerical algorithm to be used for both the nonlinear steady and the linearized unsteady flow computations. The important features of the work are the discretization of the flow domain via a single, unified edge-data structure for mixed element meshes, the use of a Laplacian operator, which results in a nearest neighbor stencil, and the full linearization of the Spalart–Allmaras turbulence model. Four different test cases are presented for the validation of the proposed method. The first one is a comparison against the classical subsonic flat plate cascade theory, the so-called LINSUB benchmark. The aim of the second test case is to check the computational results against the asymptotic analytical solution derived by Lighthill for an unsteady laminar flow. The third test case examines the implications of using inviscid, frozen-turbulence, and fully turbulent models when linearizing the unsteady flow over a transonic turbine blade, the so-called 11th International Standard Configuration. The final test case is a rotor/stator interaction, which not only checks the validity of the formulation for a three-dimensional example, but also highlights other issues, such as the need to linearize the wall functions. Detailed comparisons were carried out against measured steady and unsteady flow data for the last two cases and good overall agreement was obtained.

Accuracy, Scalability, and Efficiency of Mixed-Element USM3D for Benchmark Three-Dimensional Flows

2019 ◽  
Author(s):  
Mohagna J. Pandya ◽  
Dennis C. Jespersen ◽  
Boris Diskin ◽  
James Thomas ◽  
Neal T. Frink
Keyword(s):  
Three Dimensional ◽  
Mixed Element

Robust Conservative Level Set Method for 3D Mixed-Element Meshes — Application to LES of Primary Liquid-Sheet Breakup

2014 ◽  
Vol 16 (2) ◽  
pp. 403-439 ◽  
Author(s):  
Thibault Pringuey ◽  
R. Stewart Cant
Keyword(s):  
Experimental Data ◽  
Level Set ◽  
Multiphase Flows ◽  
Volume Fraction ◽  
Computational Cost ◽  
Three Dimensional ◽  
Liquid Sheet ◽  
Liquid Volume ◽  
Mixed Element ◽  
Conservative Level Set

AbstractIn this article we detail the methodology developed to construct an efficient interface description technique — the robust conservative level set (RCLS) — to simulate multiphase flows on mixed-element unstructured meshes while conserving mass to machine accuracy. The approach is tailored specifically for industry as the three-dimensional unstructured approach allows for the treatment of very complex geometries. In addition, special care has been taken to optimise the trade-off between accuracy and computational cost while maintaining the robustness of the numerical method. This was achieved by solving the transport equations for the liquid volume fraction using a WENO scheme for polyhedral meshes and by adding a flux-limiter algorithm. The performance of the resulting method has been compared against established multiphase numerical methods and its ability to capture the physics of multiphase flows is demonstrated on a range of relevant test cases. Finally, the RCLS method has been applied to the simulation of the primary breakup of a flat liquid sheet of kerosene in co-flowing high-pressure gas. This quasi-DNS/LES computation was performed at relevant aero-engine conditions on a three-dimensional mixed-element unstructured mesh. The numerical results have been validated qualitatively against theoretical predictions and experimental data. In particular, the expected breakup regime was observed in the simulation results. Finally, the computation reproduced faithfully the breakup length predicted by a correlation based on experimental data. This constitutes a first step towards a quantitative validation.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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