Finite Element Analysis Of The Active Soft Matter Model And Its Applications

Active soft matter refers to a class of materials with unique non-equilibrium kinetic properties that can convert energy from the surrounding environment into their own kinetic energy.These materials have important applications in drug delivery,pollution control,and the preparation of smart materials.One of the significant challenges in the study of active soft matter is the phenomenon of non-equilibrium self-organization.The main difficulty lies in the presence of multiple cooperative factors and complex competitive processes.In the first part,the existence and uniqueness of the solution of the active soft matter model is proved.Subsequently,the numerical scheme is constructed and analyzed numerically.Due to the existence of strong nonlinear terms,fourth-order term and pressure term in the model,in order to overcome the high computational cost and obtain a fully discrete numerical scheme with high efficiency,accuracy and unconditional stability,the model is rewritten as an equivalent system of second-order nonlinear coupled equations by introducing an auxiliary variable.Then,the pressure projection method is introduced to split the velocity and pressure unknowns and solve the difficulty caused by the incompressibility condition in the model.Finally,some numerical examples are given to verify the stability and convergence of the numerical scheme,and the dynamic mechanism of the self-organizing motion of the active soft matter is analyzed by comparing the numerical simulation results with the experimental results.In the second part,the self-organizing motion of active soft matter under magnetic field is considered.Firstly,the self-organizing motion model of active soft matter under the action of magnetic field is established by combining the active soft matter model with Maxwell equations,and the existence and uniqueness of the model solutions are proved.Next,the numerical scheme is constructed and analyzed numerically.Due to the existence of strong nonlinear term,fourth order term,pressure term and coupling term in the model,by introducing auxiliary variables and pressure projection method,the original equation is decomposed into two subsystems to solve the velocity and pressure respectively,and a linear,decoupled and unconditional stability fully discrete numerical scheme is given.Finally,corresponding numerical experiments are given to verify the stability and convergence of the numerical scheme,and the numerical simulation results are compared with the experimental results to analyze the dynamic mechanism of the self-organizing motion of active soft matter under the action of magnetic field.