3. Code Overview

3.1. Feature List

FLEXI currently has the following features implemented, with most of them being covered in Section 5 Tutorials.

Equation Systems

• Compressible Euler equations

• Compressible Navier-Stokes equations

• Linear scalar advection and diffusion equations

• Reynolds-averaged Navier–Stokes equations using Spalart–Allmaras turbulence model

Space Discretization

• Discontinuous Galerkin Spectral Element Method (DGSEM) [1, 2]

  • Legendre Gauss nodes

  • Legendre Gauss Lobatto nodes

• Finite Volume (FV) shock-capturing by either

  • Switching to finite volume subcells [3] or

  • Blending the finite volume operator [4]

  • Several shock indicators available

Time Discretization

• Explicit Runge-Kutta (RK) schemes

  • Standard RK schemes

  • Low storage RK schemes [5]

  • Strong stability preserving RK methods [6]

Computational Domain

• Two- or three-dimensional domains

• Curved Meshes

• Nonconforming Meshes via mortar interfaces [7]

• Sponge zone [8]

• Boundary conditions

  • Various subsonic inflow and outflow conditions [9]

  • Exact boundaries (Dirichlet)

  • Periodic boundaries

  • Slip wall (Euler wall)

  • Non-slip walls (Navier-Stokes wall): adiabatic / isothermal

Numerical Scheme

• Classical and split-form DG schemes [10]

• Dealiasing [11]

  • Filtering

  • Overintegration

• Riemann solvers

  • Local Lax-Friedrichs

  • HLL

  • HLLC

  • Roe-Pike

• Lifting methods

  • Bassi Rebay 1 [12]

  • Bassi Rebay 2 [12]

• Time averaging

3.2. Compiler Options

The following table describes the most important configuration options which can be set when building FLEXI using CMake. Some options are dependent on others being enabled (or disabled), such that the available ones may change upon reconfiguring.

Table 3.1 Compiler Options

Build Option	Possible Values	Description
CMAKE_BUILD_TYPE	Release / Profile / Debug	normal execution / performance profiling using gprof / debug compiler for detailed error messages during code development
CTAGS_PATH		install directory of Ctags, an optional program used to jump between tags in the source files (see e.g. the implementations Exuberant Ctags or Universal Ctags)
LIBS_BUILD_HDF5	on / off	will be set to on if no pre-built HDF5 installation was found on your machine to build a HDF5 version during compilation
HDF5_DIR		specify the directory of a pre-built HDF5 library that was built using the CMake system, this directory should contain the CMake configuration files (e.g. hdf5-config.cmake)
FLEXI_2D	on / off	set to on to run two-dimensional simulations, in this case you have to provide a mesh that consists of only one layer of elements in the third dimension
FLEXI_EQNSYSNAME	linearscalaradvection / navierstokes / rans_sa	linear scalar advection-diffusion equation / Navier–Stokes equations / Reynolds-averaged Navier–Stokes equations using Spalart–Allmaras turbulence model
FLEXI_FV	off / switch / blend	Finite-Volume (FV) shock-capturing: disabled / by switching DG elements in FV subcell representation [3] / by blending the FV and the DG operator [4]
FLEXI_FV_RECONSTRUCTION	on / off	only available if FLEXI_FV is set either to switch or blend, enables the linear reconstruction of the solution at the FV subcell faces (second-order FV scheme) and is needed for the calculation of parabolic gradients
FLEXI_LIFTING	br1 / br2	lifting method to compute the DG gradients in the parabolic terms: first [12] / second [13] method of Bassi and Rebay
LIBS_USE_MPI	on / off	define whether to compile with MPI (necessary for parallel execution)
FLEXI_NODETYPE	gauss / gauss-lobatto	node-set used to define the basis functions of the DG method, see [1] for details
LIBS_USE_PAPI	on / off	enable to use the PAPI library to perform performance measurements (e.g. flop counts)
FLEXI_PARABOLIC	on / off	define whether the parabolic term of the chosen equation system should be included or not, more efficient than simply setting the diffusion coefficient to zero since the gradients do not need to be discretized
FLEXI_POLYNOMIAL_DEGREE	N / {1,2,3,…}	polynomial degree of basis functions: to be set in parameter file / compile with fixed degree for performance (1,2,3,…)
FLEXI_SPLIT_DG	on / off	enable the split form of the DG operator, allows to use kinetic energy or entropy stable flux functions
FLEXI_TESTCASE	default / hit / phill / riemann2d / taylorgreenvortex / channel	some benchmark simulation setups are encapsulated in test cases (separate sub-folders) with case-specific initialization, analyze routines, boundary conditions, etc., while the default test case does not include any additions: see section Tutorials for more details
FLEXI_VISCOSITY	constant / sutherland / powerlaw	modeling approach for the dynamic viscosity: constant / Sutherland’s law / power law
POSTI	on / off	enable to also build the post-processing tool-set next to the actual simulation code, the specific tools can be selected once this flag is enabled
POSTI_VISU_PARAVIEW	on / off	enable to build the ParaView plugin for the visualization of FLEXI simulation data, the ParaView libraries must be available on the systems and environment variable $ParaView_DIR set accordingly
FLEXI_PERFORMANCE	on / off	enables a set of advanced features to improve the performance of FLEXI
FLEXI_PERFORMANCE_OPTILIFT	on / off	enable to lift only the gradients of the variables in the flux function of the selected equation system improves the performance for FLEXI_PARABOLIC=ON, but cannot be used if posti tool-set is built (POSTI=ON)
FLEXI_PERFORMANCE_PGO	on / off	enables profile-guided optimization (PGO) for compilation, currently only supported with GNU compiler the required two-step compilation process is detailed in section Performance Improvements