A decoupled Crank-Nicolson leap-frog scheme for the unsteady bioconvection flows problem with concentration dependent viscosity
By: Chenyang Li
Potential Business Impact:
Helps predict how tiny living things move in liquids.
A fully discrete Crank--Nicolson Leap--Frog (CNLF) scheme is proposed and analyzed for the unsteady bioconvection flow problem with concentration-dependent viscosity. Spatial discretization is handled via the Galerkin finite element method (FEM), while temporal discretization employs the CNLF method for the linear terms and a semi-implicit approach for the nonlinear terms. The scheme is proven to be unconditionally stable, i.e., the time step is not subject to a restrictive upper bound. Using the energy method, $L^2$-optimal error estimates are derived for the velocity and concentration . Finally, numerical experiments are presented to validate the theoretical results.
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