Towards a mesh-free computation of transport phenomena
This paper formulates a computational procedure based on the Trefftz method for the solution of nonlinear transport phenomena. This new unified approach is particularly important when solving coupled, nonlinear, inhomogenous, anisotropic, multiphase, and multifield heat and mass transfer problems. Physical system represents the general transport equation, standing for a broad spectra of mass, energy, momentum, and species transfer problems. This equation is cast into non-linear Poisson form and expanded with respect to the transport variable. Fully implicit time-discretization is used. The particular solution method is applied as a general solution framework. The solution of the inhomogenous part is based on the radial basis function global approximation, and the solution of the homogenous part is based on the Trefftz method Laplace equation fundamental solution global approximation. The discrete approximate method results in a global point-collocation based grid and hence eliminates the need for polygonization of the computational boundary and domain.
radial basis functions nonlinear transport equation method of particular solutions method of fundamental solutions collocation