METiS

METiS-USP (Morison's Equation Time domain Simulator - University of São Paulo) is a time-domain solver for the analysis of floating offshore wind turbines written in C++. By disabling some effects, it can also be applied to other floating structures or fixed offshore/onshore wind turbines.

The following effects are modeled in METiS-USP:

• Hydrodynamics: wave loads are computed using a modified version of Rainey's equation, which can be seen as an extended version of Morison's equation to include second-order wave loads acting on the floater. Drag on the structure is considered using the traditional quadratic term from Morison's equation. Details can be found in Carmo, 2021 and Carmo and Simos, 2022.
• Aerodynamics: aerodynamic loads on the rotor are included using Blade Element Momentum Theory (BEMT). Details can be found in Pegoraro, 2018 (in Portuguese) and Carmo, 2021.
• For now, body dynamics is modeled using the equations of motion of a rigid body. Moorings are not modeled yet, but their effects can be partially included by specifying a stiffness matrix and a constant vertical force.

Installing, compiling and running

Linux

Installing dependencies/third party tools:

• Ensure a C++ compiler is installed. Otherwise, a suggestion is to install g++: sudo apt-get install g++

• Install CMake: sudo apt-get install cmake

• Instal Intel (R) MKL. By the time I wrote these Linux instructions, it is part of Intel (R) oneAPI Base Toolkit, available at https://www.intel.com/content/www/us/en/developer/tools/oneapi/overview.html#gs.gdas9u

• Need to set environment variables: https://www.intel.com/content/www/us/en/develop/documentation/get-started-with-intel-oneapi-dlfd-linux/top/before-you-begin.html

• Armadillo (details in the readme file provided with Armadillo):

  1. Download at http://arma.sourceforge.net;
  2. Extract files;
  3. As MKL is probably installed in a non standard location, I had to run this extra step that is not included in the Armadillo readme file sudo ln -s /opt/intel/oneapi/mkl/latest/lib/intel64/libmkl_rt.so /usr/local/lib/libmkl_rt.so. It creates a symbolic link so that ld can find MKL;
  4. In a terminal window, change into the directory that was created by unpacking Armadillo, and type cmake . (the full stop separated from "cmake" by a space is important);
  5. Activate MKL in your current terminal window source /opt/intel/oneapi/setvars.sh
  6. Type sudo make install

Compiling and running

After installing all the previous dependencies/third party tools listed above, METiS can be compiled and linked using ./build_metis. It can then be run using ./METiS path/to/input/file.txt. Note that to use Intel MKL you have to run source /opt/intel/oneapi/setvars.sh or equivalent depending on your MKL path.

Windows

• Download Visual Studio Community or other IDE of your choice.

• The Armadillo files that need to be included are provided in /METiS/src/armadillo-version_include. Alternatively, you can download Armadillo at http://arma.sourceforge.net and copy the entire include folder to a convenient location.

• Download and install Intel (R) Math Kernel Library (MKL) at https://software.intel.com/en-us/mkl (Note: The following steps were written when MKL was not part of the OneAPI Base Toolkit, so they might need update).

• Modify include/armadillo_bits/config.hpp to indicate which libraries are currently available on your system (see the readme file provided with Armadillo for details).

• Configure a project in your IDE (the procedure below is given for Visual Studio):

  1. Create a new Empty Project;
  2. If you are using Visual Studio 2017 or above, downgrade your project to Visual Studio 2015. This is done by right clicking on the project name and selecting Properties. In Configuration Properties, find Platform Toolset and change it to Visual Studio 2015 (v140). I honestly don't know why this is necessary;
  3. Add all the files included in /src/ (except for Armadillo's include folder) to the project;
  4. Locate the MKL folder. It is usually in C:\Program Files (x86)\IntelSWTools\compiler_and_libraries_xxxx\windows\mkl;
  5. Tell the compiler to look for header files in Armadillo's and MKL's include folders. In Visual Studio 2017, right click on the project name and select properties. Unfold the C/C++ list, pick General -> Additional Include Directories, and select Edit. Use the yellow button to insert a new entry and paste the path to mkl\include directory. Do the same thing for Armadillo's include folder;
  6. Next, go to Linker -> General -> Additional Library Directories and select mkl\lib\intel64_win (select intel32_win if your computer is 32bits);
  7. Finally, you need to go to Linker -> Input -> Additional Dependencies and add mkl_core.lib, mkl_sequential.lib, and mkl_intel_lp64.lib (if 32bits, replace mkl_intel_lp64.lib by ** mkl_intel_c_dll.lib**).

Running

METiS is a CLI software. To run it on Windows, open a PowerShell window and type:

& "Path\to\METis\executable.exe" "Path\to\test_case.txt"

with the paths replaced by the ones specific to your case.