Choosing the thermal conduction equation solution method in SPH

Abstract

The set of explicit iterative schemes for parabolic problems (heat conduction as example) is reviewed. The iterative process is constructed based on algebraic polynomials (Chebyshev, Lanczos, or Legendre) properties. They combine the simplicity of explicit time-integration with the increased allowed timestep. This approach may be applied at smoothed particle hydrodynamics (SPH) simulations as a replacement for the popular implicit time-integration schemes, whose drawbacks might get stronger especially on SPH-like contrary to mesh-style space description.