Fluid Simulation Based On Frequency Method To Conserve Shape

Physical-based fluid simulation is an important part of computer graphics.Due to the complexity of fluid motions,simulating fluid of high quality costs large number of computing resource and takes long time.As the requirement of high quality and large scenes getting bigger and bigger,the animators must simulate fluids in high-resolution grid.The shape of fluid simulated in fine grid always doesn't meet what animators expect.To get the expected shape of fluids,the animators need to adjust the parameters of fluid simulation repeatedly.In addition,due to the numerical error in Computational Fluid Dynamics(CFD),the shape of fluid simulated in low-resolution grid doesn't match the fluid simulated in high-resolution grid.Keeping shape of fluids from low-resolution and high-resolution similar can help animators to get their expecting fluid shape quickly,which could help reduce the time spent on simulating fluids.With the current framework of fluid simulating,this paper analyses the reason that leads to the numerical error in advection step.According to the reasons,this paper raises two methods,which are "shape enhancement" and "shape reconstruction",to ensure fluids simulated in different resolutions of grids could have similar shape.In "shape enhancement" method,pointing at the feature that advection step in fluid simulation is equal to a low-pass filter that filters the high-frequency data;the paper raises the method of adding the high-frequency signal back by applying a high-pass filter.With related knowledge from signal processing field,the paper uses Fourier transformer to speed up the convolution step with high-pass filter kernel.In "shape reconstruction" method,the paper infers the relationship of fluid field after advection step between different resolutions of grids.Based on the theory,the paper makes a reconstruction filter between fine grids and coarse grids from frequency field.By applying the reconstruction filter to the normal fluid simulation framework,we make the shapes of fluid simulated in different resolutions of grid similar to each other.The innovation points of this paper are as follows:(1)Analyze the reasons that cause shapes of fluids simulated in different resolution of grids variable,and figure out the principle of two methods,which are shape enhancement and shape reconstruction.(2)Use the concept of filter to improve the framework of fluid simulation.(3)Both the methods,shape enhancement and shape reconstruction,could make the fluid simulated in low-resolution grid and high-resolution grid have similar shape,which helps animators to get their ideal fluid effects quickly.