Technical Description

FLEXI is a high-order accurate, open-source solver for general partial differential equations of hyperbolic/parabolic-type based on the discontinuous variant of the spectral element method (SEM), the discontinuous Galerkin (DG) spectral element method (DGSEM). This enables an element-local and efficient scheme, even on highly parallel systtems. Its primary areas of application are direct numerical and large eddy simulations (LES) of multiscale- and multi-physics problems, where the fluid phase is governed by the compressible Navier–Stokes–Fourier equations (NSE), which includes turbulent flows and shock-turbulence interaction.

FLEXI Explainer

If the above technical description was not what you’re looking for, check out the explainer answers to some common questions below.

What can FLEXI simulate?

FLEXI solves the compressible Navier-Stokes equations. These are the flow equations that can be solved to correctly predict flows with larger Mach numbers. i.e. high speed flows where objects move quickly enough to change the density of the fluid near the object wall. These types of flows occur, for example, at the cruiseing speed of aircraft or jet engines. To solve these equations, we use Large Eddy Simulations (LES) where most of the turbulent spectrum is resolved. This allows for a very good prediction of turbulent flow, which is highly relevant for almost every practical flow. At larger Mach numbers (Mach > 1, faster than the speed of sound), shocks can occur. The very large gradients in the flow field where shocks occur poses a great challenge for numerical methods. Therefore, a shock capturing method is used to ensure stability despite these large gradients in the flow field.

What are the trade-offs of using FLEXI?

FLEXI, like other codes in CEEC, is specialized in performing high-order, high-resolution simulations necessary to answer scientific questions that require, for example, the most accurate possible description of turbulence. High order simulation techniques are important for simulating the complex, nonlinear dynamics of turbulence and allow us to perform a simulation that is just as accurate as using a low order method with significantly fewer degrees of freedom.

Unlike other codes in CEEC, though, FLEXI uses the high order numerical method called the discontinuous Galerkin (DG) method to perform highly resolved flow simulations. It allows FLEXI to very efficiently use high performance computers achieving ideal scaling up to several thousand processors to solve large scale problems.  However, the DG method also allows FLEXI to focus on high speed flows, where both shock waves and turbulence can occur. Compared to other codes in CEEC, FLEXI is tailored for high speed flows – this is where it shines.

Nevertheless, the high-resolution capability for high-speed flows requires a significant amount of resources and specialized, custom-made grids. For lower flow speeds, other approaches are more efficient.

What will CEEC aim to improve about FLEXI?

Within the CEEC project, the code will be further developed to make efficient use of accelerators such as GPUs that are increasingly used in high-performance computers. Furthermore, a new approach for wall-modeled LES will be developed using machine learning methods to further increase the simulation efficiency, especially at high Reynolds numbers where a fluid’s speed and viscocity enable highly turbulant flow.

Why is this improvement a challenge?

In order to use accelerators such as GPUs efficiently, the underlying data structures in the software, which was originally developed for CPU-based systems, must be optimized. This optimization represents a major impact on the software and must be carried out carefully.

What real-world benefits will an improved FLEXI help achieve?

The turbulent, compressible flows that FLEXI can simulate are highly relevant to the aviation industry, as in the Lighthouse case of Shock – Boundary Layer Interaction and Buffet on Wings at the Edge of the Flight Envelope. Our understanding of this shock effect can be improved by numerical simulations like FLEXI with the goal of preventing or delaying its occurrence. In the longer term, data and understanding gained from FLEXI simulations could lead to increased flight safety with a simultaneous decrease in structural loading and fuel used. 

Important Links

Related Lighthouse Case

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