scholarly journals Coupling of hybridisable discontinuous Galerkin and finite volumes for transient compressible flows

2021 ◽  
Author(s):  
◽  
Sanjay Komala Sheshachala
Keyword(s):  
Discontinuous Galerkin ◽  
Compressible Flows ◽  
Transient Flow ◽  
Degree Of Approximation ◽  
High Order ◽  
Finite Volumes ◽  
Implicit Time ◽  
Wind Gust ◽  
Transient Effects ◽  
Low Order

Fast, high-fidelity solution workflows for transient flow phenomena is an important challenge in the computational fluid dynamics (CFD) community. Current low-order methodologies suffer from large dissipation and dispersion errors and require large mesh sizes for unsteady flow simulations. Recently, on the other hand, high-order methods have gained popularity offering high solution accuracy. But they suffer from the lack of robust, curvilinear mesh generators.A novel methodology that combines the advantages of the classical vertex-centred finite volume (FV) method and high-order hybridisable discontinuous Galerkin (HDG) method is presented for the simulation of transient inviscid compressible flows. The resulting method is capable of simulating the transient effects on coarse, unstructured meshes that are suitable to perform steady simulations with traditional low-order methods. In the vicinity of the aerodynamic shapes, FVs are used whereas in regions where the size of the element is too large for finite volumes to provide an accurate answer, the high-order HDG approach is employed with a non-uniform degree of approximation. The proposed method circumvents the need to produce tailored meshes for transient simulations, as required in a low-order context, and also the need to produce high-order curvilinear meshes, as required by high-order methods.FV and HDG methods for compressible inviscid flows with an implicit time-stepping method and capable of handling flow discontinuities is developed. A two-way coupling of the methods in a monolithic manner was achieved by the consistent application of the so-called transmission conditions at the FV-HDG interface. Numerical tests highlight the optimal convergence properties of the coupled HDG-FV scheme. Numeri-cal examples demonstrate the potential and suitability of the developed methodology for unsteady 2D and 3D flows in the context of simulating the wind gust effect on aerodynamic shapes.

Simulation of the Transitional Flow in a Low Pressure Gas Turbine Cascade With a High-Order Discontinuous Galerkin Method

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
A. Ghidoni ◽  
A. Colombo ◽  
S. Rebay ◽  
F. Bassi
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
High Order ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
High Reynolds

In the last decade, discontinuous Galerkin (DG) methods have been the subject of extensive research efforts because of their excellent performance in the high-order accurate discretization of advection-diffusion problems on general unstructured grids, and are nowadays finding use in several different applications. In this paper, the potential offered by a high-order accurate DG space discretization method with implicit time integration for the solution of the Reynolds-averaged Navier–Stokes equations coupled with the k-ω turbulence model is investigated in the numerical simulation of the turbulent flow through the well-known T106A turbine cascade. The numerical results demonstrate that, by exploiting high order accurate DG schemes, it is possible to compute accurate simulations of this flow on very coarse grids, with both the high-Reynolds and low-Reynolds number versions of the k-ω turbulence model.

A High-Order Discontinuous Galerkin Discretization with Multiwavelet-Based Grid Adaptation for Compressible Flows

2014 ◽  
Vol 62 (1) ◽  
pp. 25-52 ◽  
Author(s):  
Nils Gerhard ◽  
Francesca Iacono ◽  
Georg May ◽  
Siegfried Müller ◽  
Roland Schäfer
Keyword(s):  
Discontinuous Galerkin ◽  
Compressible Flows ◽  
High Order ◽  
Galerkin Discretization ◽  
Grid Adaptation

scholarly journals Performance assessment of low-order versus high-order numerical schemes in the numerical simulation of aquifer flow

2016 ◽  
Vol 47 (6) ◽  
pp. 1104-1115 ◽  
Author(s):  
A. A. Ameli ◽  
M. J. Abedini
Keyword(s):  
Numerical Methods ◽  
Transient Flow ◽  
Exact Analytical Solution ◽  
Differential Quadrature Method ◽  
High Order ◽  
Unconfined Aquifers ◽  
Node Distribution ◽  
Pumping Wells ◽  
Mesh Less ◽  
Low Order

Numerical methods have been widely used to simulate transient groundwater flow induced by pumping wells in geometrically and mathematically complex systems. However, flow and transport simulation using low-order numerical methods can be computationally expensive with a low rate of convergence in multi-scale problems where fine spatial discretization is required to ensure stability and desirable accuracy (for instance, close to a pumping well). Numerical approaches based on high-order test functions may better emulate the global behavior of parabolic and/or elliptic groundwater governing equations with and without the presence of pumping well(s). Here, we assess the appropriateness of high-order differential quadrature method (DQM) and radial basis function (RBF)-DQM approaches compared to low-order finite difference and finite element methods. This assessment is carried out using the exact analytical solution by Theis and observed head data as benchmarks. Numerical results show that high-order DQM and RBF-DQM are more efficient schemes compared to low-order numerical methods in the simulation of 1-D axisymmetric transient flow induced by a pumping well. Mesh-less RBF-DQM, with the ability to implement arbitrary (e.g., adaptive) node distribution, properly simulates 2-D transient flow induced by pumping wells in confined/unconfined aquifers with regular and irregular geometries, compared to the other high-order and low-order approaches presented in this paper.

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