RBF Morph Training Agenda Session #1 (May 24, 2:00 PM India Time, - PowerPoint PPT Presentation

RBF Morph Training Agenda Session #1 (May 24, 2:00 PM India Time, Duration - 60mins) General Introduction of RBF Morph, Features with examples Session #2 (May 29, 2:00 PM India Time, Duration - 60mins) Basic Usage of RBF Morph, Examples and Live demonstration Session #3 (June 11, 2:00 PM India Time, Duration - 60mins) Advanced Usage of RBF Morph, Multi-solve, Free surface Deformation, STL target, Back to CAD, WB coupling ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

RBF Morph Training Material Web Portal: www.rbf-morph.com frequently updated with News Download Area: http://rbf-morph.com/index.php/download • animations, technical papers, conference presentations • for registered users (usr:ANSYS_COM, pwd:ANSYS_COM) YouTube: www.youtube.com/user/RbfMorph video tutorials Documentation Package (on box.com reserved area): • User Guide / Installation Notes • Tutorials (complete of support files folders) Linkedin: http://it.linkedin.com/in/marcobiancolini E-mail support: info@rbf-morph.com ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

RBF Morph Training General Introduction of RBF Morph, Features with examples Dr. Marco Evangelos Biancolini ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

Outline • RBF Morph tool presentation • Industrial Applications • Tutorials ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

RBF Morph tool presentation ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

Morphing & Smoothing • A mesh morpher is a tool capable to perform mesh modifications , in order to achieve arbitrary shape changes and related volume smoothing, without changing the mesh topology. • In general a morphing operation can introduce a reduction of the mesh quality • A good morpher has to minimize this effect, and maximize the possible shape modifications. • If mesh quality is well preserved, then using the same mesh structure it’s a clear benefit ( remeshing introduces noise! ). ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

The Aim of RBF Morph • The aim of RBF Morph is to perform fast mesh morphing using a mesh-independent approach based on state-of-the-art RBF ( Radial Basis Functions ) techniques . • The use of RBF Morph allows the CFD user to perform shape modifications , compatible with the mesh topology, directly in the solving stage , just adding a single command line in the input file: (rbf- morph ‘(("sol -1" amp-1) ("sol-2" amp-2)...("sol-n" amp-n))) • The final goal is to perform parametric studies of component shapes and positions typical of the fluid-dynamic design like: • Design Developments • Multi-configuration studies • Sensitivity Studies • DOE (Design Of Experiment) • Optimization ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

RBF Morph Features • Add on fully integrated within Fluent (GUI, TUI & solving stage) and Workbench • Mesh-independent RBF fit used for surface mesh morphing and volume mesh smoothing • Parallel calculation allows to morph large size models (many millions of cells) in a short time • Management of every kind of mesh element type (tetrahedral, hexahedral, polyhedral, etc.) • Support of the CAD re-design of the morphed surfaces • Multi fit makes the Fluent case truly parametric (only 1 mesh is stored) • Precision : exact nodal movement and exact feature preservation ( RBF are better than FFD ). ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

Background: RBF Theory • A system of radial functions is used to fit a solution for the mesh movement/morphing, from a list of source points and their displacements . This approach is valid for both surface shape changes and volume mesh smoothing. • The RBF problem definition does not depend on the mesh • Radial Basis Function interpolation is used to derive the displacement in any location in the space, so it is also available in every grid node. • An interpolation function composed by a radial basis and a polynomial is defined.   N                     s x x x h x h x x y z i i 1 3 4  1 i ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

Background: RBF Theory        • A radial basis fit exists if desired s x g x 1 i N k k i i values are matched at source   N    0 q x points with a null poly contribution i k i  i 1 • The fit problem is associated with       γ M P g              the solution of a linear system β T       P 0 0   • M is the interpolation matrix      M x x 1 i j N ij k k i j • P is the constraint matrix   0 0 0 1 x y z   k k k 1 1 1 • g are the scalar values prescribed   0 0 0 1 x y z  k k k   P 2 2 2 at source points         0 0 0 •  and  are the fitting coefficients 1 x y z   k k k N N N ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

Background: RBF Theory  Radial Basis Function ( r ) • The radial function can be Spline type (R n ) n r , n odd fully or compactly n log Thin plate spline (TPS n ) r r , n even supported. The bi- Multiquadric(MQ) harmonic kernel fully  2 1 r Inverse multiquadric (IMQ) 1 supported gives the best  2 results for smoothing. 1 r Inverse quadratic (IQ) 1  • For the smoothing problem 2 1 r Gaussian (GS) e  2 r each component of the    displacement prescribed at N                 x x x x x  v s x x x x y z x x i k 1 2 3 4 the source points is i   i 1    N                 interpolated as a single  y y y y y v s x x x x y z y y i k 1 2 3 4  i  i 1 scalar field.    N                 z z z z z v s x x x x y z  z z i k 1 2 3 4  i  i 1 ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

Background: accelerating the solver • The evaluation of RBF at a point has a cost of order N • The fit has a cost of order N 3 for a direct fit (full populated matrix); this limit to ~10.000 the number of source points that can be used in a practical problem • Using an iterative solver (with a good pre-conditioner) the fit has a cost of order N 2 ; the number of points can be increased up to ~70.000 • Using also space partitioning to accelerate fit and evaluation the number of points can be increased up to ~ 300.000 • The method can be further accelerated using fast pre- conditioner building and FMM RBF evaluation… ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

Background: solver performances escalation • 10.000 RBF centers FIT #points 2010 2008 (Minutes) (Minutes) • 120 minutes Jan 2008 • 5 seconds Jan 2010 3.000 0 (1s) 15 • Largest fit 2.600.000 133 minutes 10.000 0 (5s) 120 • Largest model morphed 300.000.000 cells 40.000 1 (44s) Not • Fit and Morph a 100.000.000 registered cells model using 500.000 160.000 4 Not RBF centers within 15 registered minutes 650.000 22 Not • Front wing flap rotation up to registered +/-6 ° (+/-8 ° enabling Fluent 2.600.000 133 Not remeshing) registered ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

How it Works: the work-flow • RBF Morph basically requires three different steps: • Step 1 setup and definition of the problem (source points and displacements). • Step 2 fitting of the RBF system (write out .rbf + .sol). • Step 3 [SERIAL or PARALLEL] morphing of the surface and volume mesh (available also in the CFD solution stage it requires only baseline mesh and .rbf + .sol files). ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

How it Works: the problem setup • The problem must describe correctly the desired changes and must preserve exactly the fixed part of the mesh. • The prescription of the source points and their displacements fully defines the RBF Morph problem. • Each problem and its fit define a mesh modifier or a shape parameter . ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner

How it Works: the interface • One of the key aspects of RBF Morph , in respect to FLUENT integration, is related to the ability of extracting information from the FLUENT mesh and to the user interface GUI ANSYS Training 2012 www.rbf-morph.com RBF Morph, an ANSYS Inc. Partner