### What platforms are supported for M-Star CFD?¶

M-Star CFD platform compatibility is shown below for each component

• Pre-Processor: Windows

• Solver: Windows, Linux

• Post-Processor: Windows, Linux

## User Defined Expression Syntax¶

Users can define custom expressions for inlet/outlet boundary conditions, using standard C++ functions and operators

Preconfigured Functions

Name

Explanation

sin

sine function

cos

cosine function

tan

tangent function

asin

inverse sine function

acos

inverse cosine function

atan

inverse tangent function

sinh

hyperbolic sine function

cosh

hyperbolic cosine funtion

tanh

hyperbolic tangent function

asinh

inverse hyperbolic sin function

acosh

inverse hyperbolic cosine function

atanh

inverse hyperbolic tangent function

log2

logarithm to the base 2

log10

logarithm to the base 10

log

logarithm to base e (2.71828)

ln

logarithm to base e (2.71828)

exp

e raised to the power of x

sqrt

square root of a value

sign

sign function -1 if x<0; 1 if x>0; 0 if x==0

rint

round to nearest integer

abs

absolute value

min

min of all arguments

max

max of all arguments

sum

sum of all arguments

avg

mean value of all arguments

Preconfigured Operators

Name

Explanation

=

assignment

&&

logical and

||

logical or

<=

less or equal

>=

greater or equal

!=

not equal

==

equal

>

greater than

<

less than

+

-

subtraction

*

multiplication

/

division

^

raise x to the power of y

?

if then else operator

Example Velocity Expressions.

Beginning at time zero, ramp-up velocity from zero to constant value v1 over period t1 using a quarter sine wave, define:

t<t1?v1*sin(t/t1*3.1416/2.):v1


For example, increase the velocity from zero to 3 m/s over 0.6 s interval:

t<0.6?3.*sin(t/0.6*3.1416/2.):3.


Or, beginning at time zero, ramp-down velocity from v2 to zero over period t2:

t<t2?(v2*(1-sin(t/t2*3.1416/2.)):0


For example, decrease the velocity from 4 m/s to zero over 0.7 s:

t<0.7?(4.*(1-sin(t/0.7*3.1416/2.)):0


Or, to ramp up from zero velocity over period t1 to v1. Hold v1 for time period t2. Ramp-down velocity from v1 to zero over period t3:

t<t1 ? v1*sin(t/t1*3.1416/2.) : (t<(t1+t2)) ? v1 : (t<(t1+t2+t3))?(v1*(1-sin((t-t1-t2)/t3*3.1416/2.))):0


For example, to ramp up from zero velocity over period 0.8 s to 2.2 m/s. Hold 2.2 m/s for time period 1.3 s. Ramp-down velocity from 2.2 m/s to zero over period 0.1 s:

t<0.8 ? 2.2*sin(t/0.8*3.1416/2.) : ((t<(0.8+1.3)) ? v1 : (t<(0.8+1.3+0.1))? (2.2*(1-sin((t-0.8-1.3)/0.1*3.1416/2.))):0)


Example Pressure Expressions.

Beginning at time zero, ramp-up Pressure from P1 to constant value P2 over period t1 using a quarter sine wave, define:

t<t1?(P2-P1)*sin(t/t1*3.1416/2.)+P1:P2


For example, increase the pressure from 100,000 to 110,000 Pa over 0.6 s interval:

t<0.6?10000*sin(t/0.6*3.1416/2.)+100000:110000


Or, beginning at time zero, ramp-down pressure from P2 to P1 over period t2:

t<t2?(P2-(P2-P1)*(1-sin(t/t2*3.1416/2.)):P1


For example, decrease the pressure from 110,000 Pa to 100,000 Pa over 0.7 s:

t<0.7?(110000-10000.*(1-sin(t/0.7*3.1416/2.)):100000


The M-Star CFD software uses the following software libraries. Each software library is listed along with either a link to, or the complete license text reproduced in each section.

### HDF5¶

HDF5 (Hierarchical Data Format 5) Software Library and Utilities Copyright (c) 2006, The HDF Group.

NCSA HDF5 (Hierarchical Data Format 5) Software Library and Utilities Copyright (c) 1998-2006, The Board of Trustees of the University of Illinois.

Redistribution and use in source and binary forms, with or without modification, are permitted for any purpose (including commercial purposes) provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this list of conditions, and the following disclaimer.

2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions, and the following disclaimer in the documentation and/or materials provided with the distribution.

3. In addition, redistributions of modified forms of the source or binary code must carry prominent notices stating that the original code was changed and the date of the change.

4. All publications or advertising materials mentioning features or use of this software are asked, but not required, to acknowledge that it was developed by The HDF Group and by the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign and credit the contributors.

5. Neither the name of The HDF Group, the name of the University, nor the name of any Contributor may be used to endorse or promote products derived from this software without specific prior written permission from The HDF Group, the University, or the Contributor, respectively.

DISCLAIMER: THIS SOFTWARE IS PROVIDED BY THE HDF GROUP AND THE CONTRIBUTORS “AS IS” WITH NO WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED. In no event shall The HDF Group or the Contributors be liable for any damages suffered by the users arising out of the use of this software, even if advised of the possibility of such damage.

### muParser¶

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

### TinyXML¶

TinyXML is released under the zlib license:

This software is provided ‘as-is’, without any express or implied warranty. In no event will the authors be held liable for any damages arising from the use of this software.

### wxWidgets¶

wxWindows Library Licence, Version 3.1

Copyright (c) 1998-2005 Julian Smart, Robert Roebling et al

Everyone is permitted to copy and distribute verbatim copies of this licence document, but changing it is not allowed.

WXWINDOWS LIBRARY LICENCE

TERMS AND CONDITIONS FOR COPYING, DISTRIBUTION AND MODIFICATION

This library is free software; you can redistribute it and/or modify it under the terms of the GNU Library General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public License for more details.

You should have received a copy of the GNU Library General Public License along with this software, usually in a file named COPYING.LIB. If not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

EXCEPTION NOTICE

2. The exception is that you may use, copy, link, modify and distribute under your own terms, binary object code versions of works based on the Library.

3. If you copy code from files distributed under the terms of the GNU General Public License or the GNU Library General Public License into a copy of this library, as this license permits, the exception does not apply to the code that you add in this way. To avoid misleading anyone as to the status of such modified files, you must delete this exception notice from such code and/or adjust the licensing conditions notice accordingly.

4. If you write modifications of your own for this library, it is your choice whether to permit this exception to apply to your modifications. If you do not wish that, you must delete the exception notice from such code and/or adjust the licensing conditions notice accordingly.

### boost¶

Boost Software License - Version 1.0 - August 17th, 2003

Permission is hereby granted, free of charge, to any person or organization obtaining a copy of the software and accompanying documentation covered by this license (the “Software”) to use, reproduce, display, distribute, execute, and transmit the Software, and to prepare derivative works of the Software, and to permit third-parties to whom the Software is furnished to do so, all subject to the following:

The copyright notices in the Software and this entire statement, including the above license grant, this restriction and the following disclaimer, must be included in all copies of the Software, in whole or in part, and all derivative works of the Software, unless such copies or derivative works are solely in the form of machine-executable object code generated by a source language processor.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

### cub¶

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

• Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

• Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

• Neither the name of the NVIDIA CORPORATION nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL NVIDIA CORPORATION BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

### freeimage¶

This software uses the FreeImage open source image library. See http://freeimage.sourceforge.net for details.

FreeImage is used under the (GNU GPL or FIPL), version (license version).

FIPL may be found here – http://freeimage.sourceforge.net/freeimage-license.txt

### FreeType¶

This software uses in part of the work of the FreeType team.

The FTL license may be found here – https://git.savannah.gnu.org/cgit/freetype/freetype2.git/tree/docs/FTL.TXT

https://www.freetype.org/index.html

Version 2.0, January 2004

TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION

1. Definitions.

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### Tcl/Tk¶

This software is copyrighted by the Regents of the University of California, Sun Microsystems, Inc., Scriptics Corporation, and other parties. The following terms apply to all files associated with the software unless explicitly disclaimed in individual files.

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