Speaker
Description
Numerical hydrodynamics is an indispensable tool to describe the dynamics of relativistic heavy-ion reactions. Its stability is usually difficult to handle, especially in fluctuating hydrodynamics. We develop a stable implicit numerical method for solving relativistic hydrodynamics that can be more efficient than conventional explicit methods. Implicit methods are desirable considering their stability advantage compared to explicit ones. Nevertheless, they are generally considered to be computationally expensive. In this presentation, we solve this problem by introducing a fixed-point solver for the implicit Runge-Kutta methods with a new optimization through spatial stiffness detection. We implement the new implicit schemes as well as explicit ones and compare their accuracy and computational costs. We demonstrate the correctness and efficiency of the implicit methods in the case of ideal hydrodynamics by checking the convergence in the small time-step limit and comparing numerical results to the analytical solutions of the Riemann problem and the Gubser flow. The comparison is also performed in the context of heavy-ion collisions by using the TRENTo event-by-event initial conditions where viscosity is also considered. Contrary to the general expectation, we find that in these cases, the implicit scheme is more efficient for fixed accuracy than the conventional explicit methods.
| Theory / experiment | Theory |
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