Is standard symmetric formulation always better for smoothed particle hydrodynamics?

We try to demonstrate in this article that, for quasi-incompressible flows, the standard symmetric formulation of pressure gradient in smoothed particle hydrodynamics (SPH) is not necessarily superior to asymmetric ones. Comparative simulations on plane Poiseuille flows at very low Reynolds numbers show that the results using symmetric formulation are more dependent on the computational sound speed chosen, and display a larger error at the same sound speed. Our asymmetric formulation is also less sensitive to both the decrease in the smoothing length and the increase in the sound speed in simulating flows past a periodic lattice of cylinders. A preliminary explanation of the difference between symmetric and asymmetric formulations and a possible way to develop a better symmetric formulation based on our formulation are also discussed.