Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

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Session Overview
MS 20a: Fluid Applications of High-Order Finite Element Methods
Wednesday, 14/July/2021:
4:10pm - 6:10pm

Session Chair: Will Pazner
Session Chair: Matthew Joseph Zahr
Session Chair: Per-Olof Persson
Virtual location: Zoom 6

Session Abstract

Modern computational architectures have spurred recent interest in the use of a high-order finite element and discontinuous Galerkin methods for problems in computational fluid dynamics (CFD). These methods often feature low dissipation, compact stencils, and high arithmetic intensity, making them well-suited for accelerators and GPU-based architectures. Such methods have seen success when applied to challenging CFD problems such as large eddy simulation and under-resolved turbulence.

This session aims to bring together researchers from the broad field of high-order finite element methods for computational fluid dynamics in order to discuss recent developments in the areas of discretizations, solvers, and software. Specific topics of interest include shock capturing and tracking methods, stable and robust discretizations, efficient solvers and time integration (implicit, explicit, and IMEX), matrix-free algorithms, and algorithms for advanced computer architectures.

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4:10pm - 4:40pm

Implicit shock tracking using an optimization-based high-order discontinuous Galerkin method

Matthew Joseph Zahr, Tianci Huang

University of Notre Dame, United States of America

We introduce a high-order numerical method for approximating solutions of inviscid conservation laws with discontinuous solutions by tracking these features with the underlying high-order mesh without requiring additional stabilization techniques, e.,g limiting or artificial viscosity. Central to the framework is a high-order discontinuous Galerkin (DG) method of the governing equations and an optimization problem whose solution is the nodal coordinates of a feature-aligned mesh and the corresponding DG approximation to the flow; in this sense, the framework is an implicit tracking method, which distinguishes it from methods that aim to explicitly mesh relevant features. The optimization problem is solved using a novel sequential quadratic programming method that simultaneously converges the mesh and DG solution, which is critical to avoid nonlinear stability issues that would come from computing a DG solution on an unconverged (non-aligned) mesh. We use the proposed framework to solve a number of relevant two- and three-dimensional compressible flows with complex discontinuity surfaces and demonstrate the potential of the method to provide accurate approximations to these difficult problems on extremely coarse, high-order meshes.

4:40pm - 5:10pm

RANS and kL-k-log(ω) transition model in a high-order accurate discontinuous Galerkin solver

Alessandro Colombo1, Antonio Ghidoni2, Gianmaria Noventa2

1University of Bergamo, Italy; 2University of Brescia, Italy

Many reliable and robust turbulence models are nowadays available for the Reynolds Average Navier-Stokes (RANS) equations to accurately simulate a wide range of engineering flows. However, turbulence models are not able to correctly predict flow phenomena with low to moderate Reynolds numbers, which are characterized by strong transitions. Laminar-turbulent transition is common in aerospace, turbomachinery, maritime, automotive, and cooling applications. As a consequence, numerical models able to accurately predict transitional flows are mandatory to overcome the limits of turbulence models for the efficient design of many industrial applications.

Transition models in literature can be classified into low-Reynolds, non-local and local models. Low-Reynolds turbulence models have spotlighted some limitations in the prediction of the transition for general flow conditions. Non-local models are based on correlations, which relate the momentum thickness Reynolds number to local free-stream conditions, such as turbulence intensity and pressure gradient. These models can be easily calibrated in each case and can often capture correctly the major physical effects; several correlations have been developed for different transition mechanisms: natural, bypass, separation induced and crossflow transition. The main drawback lies in their non-local formulation; the information on the integral thickness of the boundary layer and the state of the flow at the edge of the boundary layer are required. Finally, the local models are based on transport equations for turbulent or transitional variable, similarly to the classical turbulence model, and require only local variables. The local formulation seems to guarantee better robustness, accuracy and easiness of implementation in modern CFD solvers. These models can be divided into empirical correlation models, proposed by Menter and Langtry, and phenomenological transition models, proposed by Walters and Leylek and based on the concept of laminar kinetic energy (LKE). The development of phenomenological models, which aim at incorporating the physics of boundary layer transition, is an attractive but challenging research field as many mechanisms influencing the flow phenomenon are not yet fully understood. Many authors proposed different variants of the three-equation phenomenological transition model based on the concept of the LKE proposed by Mayle.

These models have been proposed in the finite volume context to predict the laminar-turbulent transition, but the increasing required level of resolution naturally leads to consider discretization methods with a higher order of accuracy, such as discontinuous Galerkin (dG) methods. In dG methods, similarly to the classical continuous finite element method (FEM), the solution of the weak or variational form of a partial differential problem is approximated by polynomial functions over the elements. However, unlike continuous FEM, dG methods use an approximation that is in general discontinuous at the element interfaces, and the coupling of the approximate solutions between neighboring elements is (weakly) enforced by interface (or numerical) flux functions. An appropriate definition of the numerical flux function guarantees the consistency and stability of the dG numerical approximation. Although this higher accuracy requires an increased computational cost compared to standard finite volume methods (FVM), the compact stencil of dG spatial approximation, involving only one element and its neighbors, makes the method very well suited for massively parallel computer platforms.

In this work a new phenomenological transition model is proposed and implemented in a high-order accurate discontinuous Galerkin (dG) solver. In particular, the prediction capabilities of the kL-k-log(ω) transition model are here proved and assessed by computing turbulent flows experiencing natural, bypass and separation induced transition. In particular the model is validated by computing the flow over flat plates of the ERCOFTAC T3 series with zero/adverse pressure gradients and different values of turbulence intensity. These test cases are mainly characterized by bypass transition, due to the levels of freestream turbulence intensity Tu ≥ 1%. While to assess the model accuracy with natural and separation induced transition, the Schubauer and Klebanoff (SK) flat plate and the T3L test case of the ERCOFTAC suite, a rounded leading edge flat plate, are also simulated. Finally, the transition model is validated by computing the flow through a low-pressure turbine cascade MTU T106A and LS89 for different values of turbulence intensity. All the computations are performed in parallel by initializing the piecewise constant solution from the uniform flow at the inflow conditions and the higher-order solutions from the lower-order ones. The computed results are compared with experimental data and reference numerical solutions.

5:10pm - 5:40pm

Hybrid Schemes for High-Fidelity Simulations of High-Speed Flows

Amareshwara Sainadh Chamarthi, Steven Frankel

Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, Haifa, Israel

High-fidelity simulations of high-speed flows are of critical importance to many different engineering applications, including hypersonic aerodynamics and rocket propulsion. The ability to accurately capture both shock waves and turbulent flow structures requires a numerical scheme that has low dissipation and dispersion features. It is difficult for a single scheme to accommodate both of these requirements. Hence hybrid schemes have been used in the past to address this. Recently, a spectral-difference scheme has been introduced with WENO-type interpolation to handle shocks. While accurate, this scheme is computationally expensive and could benefit from using a shock sensor in the context of a hybrid scheme. In this study, we explore two different approaches to address this shortcoming. The first is related to using the BVD algorithm in the context of the finite-volume scheme, and the second is related to combining a linear spectral difference with the aforementioned non-linear scheme. Standard test cases in 1D and 2D will be used to illustrate the efficacy of these schemes. The issue of positivity-preserving of the thermodynamic variables will also be discussed.

5:40pm - 6:10pm

A direct discontinuous Galerkin method for compressible Navier-Stokes equations

Mustafa Engin Danis, Jue Yan

Iowa State University, United States of America

We propose a new direct discontinuous Galerkin method with interface correction (DDGIC) for 2D compressible Navier-Stokes equations. The new DDGIC method is based on the observation that the nonlinear diffusion of Navier-Stokes equations can be represented as a certain combination of multiple individual diffusion processes corresponding to each equation and conserved variable in the system. This new representation greatly simplifies the numerical viscous flux design such that it only requires employing the simple direct DG numerical flux formula to compute the gradients of the conserved variables at the element interfaces. We also present how the new method can be used for the scalar nonlinear diffusion equations as well as a more complicated system of equations with nonlinear diffusion, i.e., turbulence simulations. We also demonstrate the high order of accuracy of the new DDGIC method for several numerical experiments.

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