We present semi-analytical solutions for the evolution of both the temperature and chemical potentials for viscous Gubser flow with conserved charges. Such a solution can be especially useful in testing numerical codes intended to simulate relativistic fluids with large chemical potentials. The freeze-out hypersurface profiles for constant energy density are calculated, along with the corresponding normal vectors, and presented as a new unit test for numerical codes. We also compare the influence of the equation of state on the semi-analytical solutions. We benchmark the newly developed smoothed particle hydrodynamics code ccake that includes both shear viscosity and three conserved charges. The numerical solutions are in excellent agreement with the semi-analytical solution and are also able to accurately reproduce the hypersurface at freeze-out.

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• Hydrodynamic models
• Quark-gluon plasma
• Lagrangian particle tracking
• Relativistic hydrodynamics