Study On Dynamics Of Spiral Waves And Their Control By Lattice Boltzmann Method

Spiral wave is the most common type of patterns,widely existing in mathematics,physics,mechanics,astronomy,chemistry,biology,medicine and other disciplines.It is very important to study the mechanism of instability and its control of spiral waves because it is harmful in many practical systems.The lattice Boltzmann method(LBM)derived from the mesoscopic theory has achieved great success in the numerical simulation of many complex systems.Apart from simulating complex fluid flow,LBM can also be used to solve the nonlinear partial differential equations.In this paper,we use the lattice Boltzmann method and the computer visualization technology to design and develop the corresponding software for simulating the spiral wave nonlinear phenomenon.The spiral wave local control,the spiral wave instability caused by the linear shear flow,the synchronization and crushing phenomena of the two layer spiral wave system and the adjustment control of the three dimensional spiral wave parameters are studied emphatically.The main work of the thesis includes the following five aspects.(1)The lattice Boltzmann method for spiral wave evolution is established,and the Barkley algorithm is compared to verify the correctness of the algorithm.The algorithm has been tested for grid independency,Numerical results show that compared with D2Q9 model,D2Q5 algorithm is more efficient.Based on the analysis of Barkley’s open source EZ-Spiral,a spiral wave simulation software LB-Spiral with lattice Boltzmann algorithm was developed.The software has the interaction,real time visualization function and real time extraction of spiral tip,which is very convenient for studying the evolution of spiral wave.The motion of two dimensional spiral wave head is studied:simple periodic rotation and roaming motion.(2)The lattice Boltzmann model with convective term is established,and the correct-ness of the model is proved by multi-scale expansion.The wave width variation of the spiral wave under the influence of convection is analyzed theoretically.By LB-Spiral software,the movement and breaking of spiral wave are studied.Under the influence of the shearing force,the spiral wave pattern is squeezed,the orbit of spiral wave changes,and moves in the opposite direction of the shear flow.When the shearing force is large,the spiral wave begins to break from the surroundings and evolves into the space-time chaotic state.When the shearing force is small,the spiral wave pattern changes,but it can’t be broken.(3)The feedback local control of two-dimensional spiral wave are studied.For the two dimensional spiral feedback control,we choose the appropriate rectangular feedback control region,using the lattice Boltzmann method to simulate.For a different size of the feedback region,with the decrease of the length of the rectangular feedback region,the time steps of the spiral wave disappear increase,but the increase is not too obvious.In the case where the spiral wave can be eliminated,the minimum length of the feedback region can be taken as 1.2 units.In the case where the spiral wave is eliminated,the closer the feedback area is to the center of the spiral wave,the smaller the minimum length required for the feedback region.The larger the relative scale of the two variables of the system,the faster the spiral wave is eliminated.Numerical simulation results show that the use of spiral wave can be controlled by low amplitude signal and small region.(4)The coupling lattice Boltzmann model of double spiral wave is established by two Bar-Eiswirth systems.The first case,we carried out a point-to-point coupling model,the initial state of the first layer is a spiral wave,and the second layer is the resting state.When the coupling strength is large,the width of the first spiral wave can be gradually reduced,When the second layer of spiral waves has not been fully excited into a synchronic state,the first layer of spiral waves is broken or disappeared.When the coupling strength is small,the two-layer system to achieve similar synchronization state after a period of evolution.The second case is local coupling.The lattice point of each column on a layer of media is coupled to the center point of the corresponding layer and the other eight lattice points.The initial states of the two layers of spiral waves are separated by a quarter of the spiral period.The two layers of spiral waves can be synchronized by the appropriate coupling strength.When the coupling strength increases,there will be spiral wave roaming and drift,resulting in two spiral waves are not synchronized,and the coexistence of spiral waves,plane waves and spatiotemporal chaos is observed.By the above study,we can use double system drive to control the spiral wave.(5)The lattice Boltzmann model for three dimensional spiral wave is established.Through the research of Barkley’s open source EZ-Scroll,the scroll wave simulation soft-ware LB-Scroll is designed by the Marching Cubes algorithm and OpenGL for 3D render-ing.The filament of scroll is simulated by LB-Scroll,the motion of the filament is analyzed and the scroll wave evolution is further studied.By the phenomenon of resonant wave drift,we adjust the model parameters to move the scroll wave to the boundary,and make it disap-pear.In summary,this thesis takes spiral wave dynamics and its control as the research background.Aiming at the mechanical properties of spiral wave dynamics,a stable and efficient LBM is developed.In addition,the detailed numerical simulation of spiral wave control is performed by the proposed coupled lattice Boltzmann method.This work has made some meaningful innovations and attempts in the study of spiral wave dynamics and its control mechanism and application by LBM.This work has broadened out the appli-cation of the lattice Boltzmann method,also facilitates the subsequent study of spiral waves.