Low shear diffusion central schemes for particle methods

We present the first application of a central scheme in an unstructured meshless code and extend it to limit diffusion in shearing flows. Some numerical diffusion is required in simulations of compressible fluids to maintain stability and prevent formation of spurious structures. The Kurganov-Tadmor (KT) central scheme uses a signal velocity and a linear reconstruction of fields to limit numerical diffusion away from discontinuities. We implement the KT scheme as a drop-in replacement for the Riemann solver in the GIZMO hydrodynamics code. Both the original finite-volume version of the KT scheme, which is quasi-Lagrangian in meshless geometry, as well as a new fully-Lagrangian finite-mass variant are presented. In addition, to mitigate excessive diffusion, a new shear-based switch is proposed. The new methods, as well as the default Riemann solver, were applied to a set of test problems. The results show that, although the KT scheme is more diffusive than the Riemann solver, it produces correct results with better convergence. The switch is shown to reduce diffusion in shearing cases, while not compromising stability in the supersonic regime. The fully-Lagrangian variant is shown to behave similarly to its Riemann solver counterpart. We conclude that the new variants of the KT scheme are good alternatives to Riemann solvers in meshless geometry, especially where its simplicity is desirable, such as for a complex equation of state.