Numerical analysis of thermo-fluid problems in 3D domains by means of the RBF-FD meshless method

Abstract

The use of CAE (Computer Aided Engineering) software, commonly applied to the design and verification of a great variety of manufactured products, is totally reliant on accurate numerical simulations. Classic mesh-based methods, e.g., Finite Element (FEM) and Finite Volume (FVM), are usually employed for such simulations, where the role of the mesh is crucial for both accuracy and time consumption issues. This is especially true for complex 3D domains which are typically encountered in most practical problems. Meshless, or meshfree, methods have been recently introduced in order to replace the usual mesh with much simpler node distributions, thus purifying the data structures of any additional geometric information. Radial Basis Function-Finite Difference (RBF-FD) meshless methods have been shown to be able to easily solve problems of engineering relevance over complex-shaped domains with great accuracy, with particular reference to fluid flow and heat transfer problems. In this paper the RBF-FD method is employed to solve heat transfer problems with incompressible, steady-state laminar flow over 3D complex-shaped domains. The required node distributions are automatically generated by using a meshless node generation algorithm, which has been specifically developed to produce high quality node arrangements over arbitrary 3D geometries. The presented strategy represents therefore a fully-meshless approach for the accurate and automatic simulation of thermo-fluid problems over 3D domains of practical interest.

Accurate Stabilization Techniques for Rbf-Fd Meshless Discretizations with Neumann Boundary Conditions

“…The boundary is characterized by locally convex and concave features with varying curvature, designed to trigger ill-conditioning issues described in section 3. A Lagrange multiplier is employed to solve the linear systems arising from the RBF-FD discretization of equation (72) since Neumann BCs are prescribed on the whole boundary [44]. The pseudocode for the stability test is presented in Algorithm 1.…”

A Distributed Model for Computing 3D Mesh Local Descriptors Based on k-Rings

“…Sometimes this problem is addressed using compact data structures for space optimization (Chen et al, 2009;Zamolo et al, 2022;Herath et al, 2020;Cignoni et al, 2003;Aleardiet al, 2005;Gurung et al, 2011;Luffel et al, 2014;Gurung et al, 2013;Rocca et al, 2011), but decreasing processing speed.…”