A Coupled Overset Mesh and Hybridizable Discontinuous Galerkin Algorithm for Pseudo-Compressible Flow

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Justin A. Kauffman ◽  
Jonathan S. Pitt
Keyword(s):  
Discontinuous Galerkin ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Optimal Order ◽  
Isentropic Flow ◽  
Hybridizable Discontinuous Galerkin ◽  
Manufactured Solutions ◽  
Preliminary Validation ◽  
Original Presentation

Abstract A previously presented overset mesh enabled hybridizable discontinuous Galerkin (HDG) finite element method is extended in this work to an isentropic compressible (pseudo-compressible) fluid. This formulation is a first-principles approach and is complementary to the augmented Lagrangian approach that was utilized in the previous HDG incompressible Navier–Stokes formulations which eliminate the global pressure field. This is the first original presentation combining overset meshes, HDG, and fluid flow, specifically isentropic flow for low Mach number applications. Verification of the code implementation of the proposed overset-HDG formulation is performed via the method of manufactured solutions (MMS) on a successively refined overset mesh configuration containing five meshes, and for order k=1,…,4, Lagrange polynomial elements in both two and three dimensions. Optimal order convergence, k + 1, can be observed in all fields for both the two- and three-dimensional simulations, for each mesh. A two-dimensional benchmark problem is also presented to enable code-to-code comparison as a preliminary validation exercise.

scholarly journals Numerical simulation of Faraday waves

2009 ◽  
Vol 635 ◽  
pp. 1-26 ◽  
Author(s):  
NICOLAS PÉRINET ◽  
DAMIR JURIC ◽  
LAURETTE S. TUCKERMAN
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Oscillation Period ◽  
Finite Amplitude ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Faraday Waves ◽  
Temporal Behaviour ◽  
Two Fluids ◽  
Front Tracking Method

We simulate numerically the full dynamics of Faraday waves in three dimensions for two incompressible and immiscible viscous fluids. The Navier–Stokes equations are solved using a finite-difference projection method coupled with a front-tracking method for the interface between the two fluids. The critical accelerations and wavenumbers, as well as the temporal behaviour at onset are compared with the results of the linear Floquet analysis of Kumar & Tuckerman (J. Fluid Mech., vol. 279, 1994, p. 49). The finite-amplitude results are compared with the experiments of Kityk et al (Phys. Rev. E, vol. 72, 2005, p. 036209). In particular, we reproduce the detailed spatio-temporal spectrum of both square and hexagonal patterns within experimental uncertainty. We present the first calculations of a three-dimensional velocity field arising from the Faraday instability for a hexagonal pattern as it varies over its oscillation period.

Three-Dimensional Numerical Prediction of the Hydrodynamic Loads and Motions of Offshore Structures

2000 ◽  
Vol 122 (4) ◽  
pp. 294-300 ◽  
Author(s):  
Karl W. Schulz ◽  
Yannis Kallinderis
Keyword(s):  
Flow Structure ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Structural Response ◽  
Offshore Structures ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Hydrodynamic Loads ◽  
Drag Coefficients ◽  
Lift And Drag

A generalized numerical method for solution of the incompressible Navier-Stokes equations in three-dimensions has been developed. This solution methodology allows for the accurate prediction of the hydrodynamic loads on offshore structures, which is then combined with a rigid body structural response to address the flow-structure coupling which is often present in offshore applications. Validation results using this method are first presented for fixed structures which compare the drag coefficients of sphere and cylinder geometries to experimental measurements over a range of subcritical Reynolds numbers. Additional fixed structure results are then presented which explore the influence of aspect ratio effects on the lift and drag coefficients of a bare circular cylinder. Finally, the spanwise flow variations between a fixed and freely vibrating cylindrical structure are compared to demonstrate the ability of the flow-structure method to correctly predict correlation length increases for a vibrating structure. [S0892-7219(00)00904-3]

scholarly journals Simulation of 3D-Unsteady Stator/Rotor Interaction in Turbomachinery Stages of Arbitrary Pitch Ratio

1996 ◽  
Author(s):  
Alexander R. Jung ◽  
Jürgen F. Mayer ◽  
Heinz Stetter
Keyword(s):  
Pressure Fluctuations ◽  
Three Dimensional ◽  
Solution Process ◽  
Computational Method ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Spanwise Direction ◽  
Time Stepping ◽  
Flow Phenomena ◽  
Pitch Ratio

This paper presents a computational method for the calculation of unsteady three-dimensional viscous flow in turbo-machinery stages. The method is based on a Finite-Volume Navier-Stokes solver for structured grids in a multiblock topology. The meshes at the stator/rotor interface are overlapped by two grid cells. An implicit residual smoothing method applicable to global time-stepping is used to accelerate the solution process. The problem of periodic boundary treatment for unequal pitches is handled using a method of time-inclined computational domains for three dimensions. The method applies a time transformation to the stator domain and to the rotor domain and uses different time-steps in the two domains. The results of a numerical simulation of the flow in a transonic turbine stage with a pitch ratio of 1.364 are presented. The time-averaged solution is compared to experimental data and satisfactory agreement is stated. Complex 3D-unsteady flow phenomena (shock motion, vortex shedding) are observed. Unsteady blade pressure fluctuations at various positions in spanwise direction are shown and the fluctuations are found to vary considerably along span. Instantaneous distributions of static pressure, Mach number, and entropy are presented.

scholarly journals Analysis of a hybridizable discontinuous Galerkin method for the Maxwell operator

2019 ◽  
Vol 53 (1) ◽  
pp. 301-324 ◽  
Author(s):  
Gang Chen ◽  
Jintao Cui ◽  
Liwei Xu
Keyword(s):  
Discontinuous Galerkin ◽  
Maxwell Equations ◽  
Numerical Solutions ◽  
Special Treatment ◽  
Optimal Order ◽  
General Regularity ◽  
Maxwell Operator ◽  
Low Regularity ◽  
Hybridizable Discontinuous Galerkin ◽  
Theoretical Results

In this paper, we study a hybridizable discontinuous Galerkin (HDG) method for the Maxwell operator. The only global unknowns are defined on the inter-element boundaries, and the numerical solutions are obtained by using discontinuous polynomial approximations. The error analysis is based on a mixed curl-curl formulation for the Maxwell equations. Theoretical results are obtained under a more general regularity requirement. In particular for the low regularity case, special treatment is applied to approximate data on the boundary. The HDG method is shown to be stable and convergence in an optimal order for both high and low regularity cases. Numerical experiments with both smooth and singular analytical solutions are performed to verify the theoretical results.

Three-Dimensional Navier-Stokes Computation of Turbomachinery Flows Using an Explicit Numerical Procedure and a Coupled k-ε Turbulence Model

1991 ◽  
Author(s):  
R. F. Kunz ◽  
B. Lakshminarayana
Keyword(s):  
Reynolds Number ◽  
Turbulence Model ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Secondary Flows ◽  
Three Dimensions ◽  
Quality Data ◽  
Navier Stokes ◽  
Evaluation Procedure ◽  
Pressure Probe

An explicit, three-dimensional, coupled Navier-Stokes/k-ε technique has been developed and successfully applied to complex internal flow calculations. Several features of the procedure, which enable convergent and accurate calculation of high Reynolds number two-dimensional cascade flows have been extended to three-dimensions, including a low Reynolds number compressible form of the k-ε turbulence model, local timestep specification based on hyperbolic and parabolic stability requirements, and eigenvalue and local velocity scaling of artificial dissipation operators. A flux evaluation procedure which eliminates the finite difference metric singularity, at leading and trailing edges, on H- and C-grids, is presented. The code is used to predict the pressure distribution, primary velocity and secondary flows in an incompressible, turbulent curved duct flow for which CFD validation quality data is available. Also, a subsonic compressor rotor passage, for which detailed laser, rotating hot-wire and five-hole pressure probe measurements have been made is computed. Detailed comparisons between predicted and measured core flow and near wall velocity profiles, wake profiles, and spanwise mixing effects downstream of the rotor passage are presented for this case. It is found that the technique provides accurate and convergent engineering simulation of these complex turbulent flows.

Three-dimensional natural convection in a box: a numerical study

1977 ◽  
Vol 83 (1) ◽  
pp. 1-31 ◽  
Author(s):  
G. D. Mallinson ◽  
G. De Vahl Davis
Keyword(s):  
Natural Convection ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Aspect Ratios ◽  
Inertial Interaction ◽  
Longitudinal Temperature

The solution of the steady-state Navier–Stokes equations in three dimensions has been obtained by a numerical method for the problem of natural convection in a rectangular cavity as a result of differential side heating. In the past, this problem has generally been treated as though it were two-dimensional. The solutions explore the three-dimensional motion generated by the presence of no-slip adiabatic end walls. For Ra = 104, the three-dimensional motion is shown to be the result of the inertial interaction of the rotating flow with the stationary walls together with a contribution arising from buoyancy forces generated by longitudinal temperature gradients. The inertial effect is inversely dependent on the Prandtl number, whereas the thermal effect is nearly constant. For higher values of Ra, multiple longitudinal flows develop which are a delicate function of Ra, Pr and the cavity aspect ratios.

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