Boundary Projection Acceleration: A New Approach to Synthetic Acceleration of Transport Calculations

A new class of synthetic acceleration methods, which can be applied to transport calculations regardless of geometry, discretization scheme, or mesh shape, is presented. Unlike other synthetic acceleration methods that base their acceleration on P₁ equations, these methods use acceleration equations obtained by projecting the transport solution onto a coarse angular mesh only on cell boundaries. It is demonstrated, via Fourier analysis of a simple model problem as well as numerical calculations of various problems, that the simplest of these methods are unconditionally stable with spectral radius ≤c/3 (c being the scattering ratio), for several different discretization schemes in slab geometry.