The stabilized biconjugate gradient algorithm BiCGStab recently presented by van der Vorst is applied to the inversion of the lattice fermion operator in the Wilson formulation of lattice Quantum Chromodynamics. Its computational efficiency is tested in a comparative study against the conjugate gradient and minimal residual methods. Both for quenched gauge configurations at β=6.0 and gauge configurations with dynamical fermions at β=5.4, we find BiCGStab to be superior to the other methods. BiCGStab turns out to be particularly useful in the chiral regime of small quark masses.

Summary A modification of the Roe scheme called L2Roe for low dissipation low Mach Roe is presented. It reduces the dissipation of kinetic energy at the highest resolved wave numbers in a low Mach number test case of decaying isotropic turbulence. This is achieved by scaling the jumps in all discrete velocity components within the numerical flux function. An asymptotic analysis is used to show the correct pressure scaling at low Mach numbers and to identify the reduced numerical dissipation in that regime. Furthermore, the analysis allows a comparison with two other schemes that employ different scaling of discrete velocity jumps, namely, LMRoe and a method of Thornber et al. To this end, we present for the first time an asymptotic analysis of the last method. Numerical tests on cases ranging from low Mach number (M∞=0.001) to hypersonic (M∞=5) viscous flows are used to illustrate the differences between the methods and to show the correct behavior of L2Roe. No conflict is observed between the reduced numerical dissipation and the accuracy or stability of the scheme in any of the investigated test cases. Copyright © 2015 John Wiley & Sons, Ltd.

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