Anisotropic diffusion in mesh-free numerical magnetohydrodynamics

Anisotropic diffusion in mesh-free numerical magnetohydrodynamics

We extend recently developed mesh-free Lagrangian methods for numerical magnetohydrodynamics (MHD) to arbitrary anisotropic diffusion equations, including: passive scalar diffusion, Spitzer–Braginskii conduction and viscosity, cosmic ray diffusion/streaming, anisotropic radiation transport, non-ideal MHD (Ohmic resistivity, ambipolar diffusion, the Hall effect) and turbulent ‘eddy diffusion’. W...

Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics

On adaptive anisotropic mesh optimisation for convection-diffusion problems

Numerical solution of convection-dominated problems requires the use of layer-adapted anisotropic meshes. Since a priori construction of such meshes is difficult for complex problems, it is proposed to generate them in an adaptive way by moving the node positions in the mesh such that an a posteriori error estimator of the overall error of the approximate solution is reduced. This approach is f...

3D-Mesh denoising using an improved vertex based anisotropic diffusion

This paper deals with an improvement of vertex based nonlinear diffusion for mesh denoising. This method directly filters the position of the vertices using Laplace, reduced centered Gaussian and Rayleigh probability density functions as diffusivities. The use of these PDFs improves the performance of a vertex-based diffusion method which are adapted to the underlying mesh structure. We also co...

Anisotropic Mesh Refinement for Three-dimensional Diffusion Simulation

We present a computational method for locally adapted conformal anisotropic tetrahedral mesh refinement. The element size is determined by an anisotropy function which is governed by an error estimation driven ruler according to an adjustable maximum error. Anisotropy in refinement is taken into account to reduce the amount of elements compared to strict isotropic refinement. The spatial resolu...