Structure of an adaptive grid computational method from the viewpoint of dynamic chaos

An attempt has been made to study the structure of an adaptive grid computational method for fluid dynamics based on the viewpoint of dynamical chaos. A simple one-dimensional convection-diffusion equation is used as the model problem. The emphasis here is not on the completeness of the results in all the parameter space, but the usefulness of the techniques utilized to study chaos for the area of computational fluid dynamics. It is demonstrated that a rich variety of patterns of the structure of the adaptive grid method can be observed, depending on the values of the preassigned parameters and Reynolds number. Both the equilibrium state and persistently chaotic state of the grid distribution can be obtained. With the same set of parameters, the basic structure of the adaptive grid method remains unchanged for a wide span of Reynolds number, but the randomness appears to increase with the Reynolds number. Besides, the intermittency scenario has also been observed. The findings from the study of the present simple model problem suggest the possibility of shedding new insights into computational fluid dynamics.