Numerical analysis demonstrates unconditionally optimal error estimates in bioconvection fluid models, highlighting reliable simulations of microorganism flow dynamics.
In this paper, the coupled and decoupled BDF2 finite element discrete schemes are obtained for the time-dependent bioconvection flows problem with concentration dependent viscosity, which consists of the Navier-Stokes equations and a linear convection-diffusion equation modeling the concentration of microorganisms in a culture fluid. The unconditionally optimal error estimate for the velocity and concentration in L²-norm are proved by using finite element approximations in space and finite differences in time. Finally, the numerical results for different viscosity are shown to support the theoretical analysis.
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Li et al. (2026) studied this question.
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