A high-resolution finite-difference method for simulating two-fluid, viscoelastic gel dynamics

► Study concerns a gel model with a polymer network immersed in a fluid solvent. ► Model is applicable to many biological systems. ► First numerical method for treating the whole coupled system of equations. ► The method is efficient and robust over a wide range of parameters. ► Applies to gels with widely varying rheologies: viscoelastic fluid to viscoelastic solid. ► Numerical results confirm the method is second order accurate in space and time.