Mesh Morphing (RBF)

What is Mesh morphing (RBF)?

Mesh morphing involves adapting a computational grid adopted for computer-aided engineering (CAE). For instance, the solid or shell mesh of a structural part ready to be processed by an FEA solver, or the volume mesh complete with boundary conditions for a CFD solver, can take a new shape by just updating nodal positions. This means that the mesh’s topology (nodes count, cells count, connectivity) stays the same. Only the nodes’ x,y, and z coordinates in the part of the model undergoing a shape modification are updated. Mesh morphing can be used for different purposes: create shape parameters (i.e., change a length, an angle a thickness), move onto a new known shape (i.e., as manufactured, as designed by CAD), move onto a body predicted by the CAE solution (automatic shape optimization with adjoint or BGM), and support multiphysics (move CFD mesh according to the evolution of the FEM-connected one, enable erosion/deposition).

Usually, mesh morphing is faster than remeshing for many reasons: it avoids “meshing noise” (having the same mesh adapted means the effect of a parameter is not confused with the impact of a new mesh structure), so variation effects can be assessed even with a coarser mesh. The CAE model can be updated in the background keeping all the original settings (boundary conditions). The update of nodal positions usually requires less computational effort vs. a complete mesh regeneration. Creating shape parameters with mesh morphing is faster than creating a parametric CAD model.

RBFs are a mathematical tool capable of interpolating available fields on a cloud of points. Mesh morphing defines a displacement field on a cloud of source points (usually some of the surfaces/curves of the CAE mesh). It then propagates it on a cloud of target points (usually the nodes of the volume/surface mesh of the CAE model undergoing adaption). The method fits very well with mesh morphing needs: its meshless nature allows you to easily manage partitioned meshes used for high-performance parallel computation (HPC); its node-wise nature will enable you to have complete control of specific areas. The computational cost of RBF can be very high, so specific algorithms (Fast Radial Basis Functions) are required to enjoy such benefits for industrial applications.

Reduced-order models (ROM), as suggested by their name, are numerical models of a system (fluid, structure, or other physics) capable of working very fast (typically in real-time). ROM is defined by adopting data-compression algorithms and applying them to many different instances (also known as snapshots) of the original model to be reduced.

RBF and ROM are not intended to improve meshing but rather allow for a link between CAE/meshing and the implementation of real-time Digital Twins. RBF is, in fact, a method of mesh morphing that supports the automatic generation of shape variations of the original mesh. Some distortion of the cells undergoing the deformation (stretching/compression) usually occurs, and a suitable mesh morphing method must preserve the quality of the morphed mesh. RBF is proven to be one of the best solutions nowadays available to implement high-quality mesh morphing: the core of the mesh is adapted with minimum distortion, and the distribution of mesh size close to the surfaces (boundary layers to capture the flow, refinement layers to capture stress raisers) is very well preserved.

mesh morphing

Mesh morphing simulations in ANSYS Fluent software

The add-on version of RBF Morph allows for shape optimization studies entirely within ANSYS Fluent by morphing an existing mesh. Main features of the RBF Mesh Morph add-in include:

User Interface: dedicated GUI and TUI.

Process Integration: morphing directly inside the solving stage without modifying the geometry, regenerating the mesh, and setting up the case again.

Mesh Topology: Modifying the original surface and volume mesh produces a nodal smoothing without changing the mesh topology.

Surface Morphing: surface meshes can be modified by free surface deformation, rigid movement, or scaling.

Volume Smoothing: high-quality smoothing the volume mesh with relatively large movements possible in a single step deformation.

Versatility: nodal smoothing is achieved using a meshless approach independent from the mesh structure, handling every kind of mesh element type (tetrahedral, hexahedral, polyhedral, prismatic, hex-core, non-conformal interfaces, etc.).

Reusability: the RBF solution can be applied to any mesh representing the same geometry.

Consistency: mesh characteristics are preserved, so mesh consistency is ensured (element size, type, and distribution, prism layers, etc.).

Parallelism: parallel calculation for large models (many millions of cells).

Efficiency: flow solutions are fully readable through all the morphed mesh, reducing the number of iterations to converge.

Precision: exact movement is ensured for the moving nodes’ locations and exact feature preservation.

Parameterization: multi-parameter and multi-step problems.

MR-CFD, an expert in the field of mesh morphing

With several years of experience simulating a wide range of problems in various CFD fields using Fluent software, the MR-CFD team is ready to offer extensive modeling, meshing, and simulation services. Simulation Services for RBF Mesh Morph are categorized as follows:

  • Optimization of different structures
  • Parametric investigation of various factors affecting a system

You may find the related products in the categories mentioned above in our CFD shop by clicking on the following link:

Our services are not limited to the mentioned subjects, and the MR-CFD team is ready to undertake different and challenging projects in the RBF Mesh Morph ordered by our customers. You can consult with our experts freely and without charge at first, and then order your project by sending the problem details to us using the following address.

[email protected]

By entrusting your project to the MR-CFD team, you will not only receive the related project’s files (Geometry, Mesh, Fluent files). Also, you will be provided with an extensive tutorial video demonstrating how you can create the geometry, mesh, and define the needed settings in the Fluent software all by yourself. And these all come with post-technical support from the MR-CFD team.

MR-CFD experts are ready to fulfill every Computational Fluid Dynamic (CFD) needs. Our service includes industrial and academic purposes considering a wide range of CFD problems. MR-CFD serves in three main categories: ANSYS Fluent Consultation, ANSYS Fluent Training, and ANSYS Fluent Project Simulation. MR-CFD company has gathered experts from various engineering fields to ensure the quality of CFD services. Your CFD project would be done in the shortest time, with the highest quality and reasonable cost.


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