Self-adaptive spherical wavelets for angular discretizations of the Boltzmann transport equation

A new method for applying anisotropic resolution in the angular domain of the Boltzmann transport equation is presented. The method builds on our previous work in which two spherical wavelet bases were developed for representing the direction of neutral particle travel. The method proposed here enables these wavelet bases to vary their angular approximations so that fine resolution may be applied only to the areas of the unit sphere (representing the direction of particle travel) that are important. We develop an error measure that operates in conjunction with the wavelet bases to determine this importance. A procedure by which the angular resolution is gradually refined for steady-state problems is also given. The adaptive wavelets are applied to three test problems that demonstrate the ability of the wavelets to resolve complex fluxes with relatively few functions, and to achieve this a particular emphasis is placed on their ability to approximate particle streaming through ducts with voids. It is shown that the wavelets are capable of applying the appropriate resolution (as dictated by the error measure) to the directional component of the angular flux at all spatial positions. This method therefore offers a new and highly efficient adaptive angular approximation method.