We study the simulation of specular reflection in a level set method implementation for wavefront propagation in high frequency acoustics using WENO spatial operators.To implement WENO efficiently andmaintain converge...We study the simulation of specular reflection in a level set method implementation for wavefront propagation in high frequency acoustics using WENO spatial operators.To implement WENO efficiently andmaintain convergence rate,a rectangular grid is used over the physical space.When the physical domain does not conformto the rectangular grid,appropriate boundary conditions to represent reflection must be derived to apply at grid locations that are not coincident with the reflecting boundary.A related problem is the extraction of the normal vectors to the boundary,which are required to formulate the reflection condition.A separate level set method is applied to pre-compute the boundary normals which are then stored for use in the wavefront method.Two approaches to handling the reflection boundary condition are proposed and studied:one uses an approximation to the boundary location,and the other uses a local reflection principle.The second method is shown to produce superior results.展开更多
In this paper,we investigate the dynamic process of liquid bridge formation between two parallel hydrophobic plates with hydrophilic patches,previously studied in[1].We propose a dynamic Hele-Shaw model to take advant...In this paper,we investigate the dynamic process of liquid bridge formation between two parallel hydrophobic plates with hydrophilic patches,previously studied in[1].We propose a dynamic Hele-Shaw model to take advantage of the small aspect ratio between the gap width and the plate size.A constrained level set method is applied to solve the model equations numerically,where a global constraint is imposed in the evolution[2]stage together with local constraints in the reinitialization[3]stage of level set function in order to limit numerical mass loss.In contrast to the finite element method used in[2],we use a finite difference method with a 5th order HJWENO scheme for spatial discretization.To illustrate the effectiveness of the constrained method,we have compared the results obtained by the standard level set method with those from the constrained version.Our results show that the constrained level set method produces physically reasonable results while that of the standard method is less reliable.Our numerical results also show that the dynamic nature of the flow plays an important role in the process of liquid bridge formation and criteria based on static energy minimization approach has limited applicability.展开更多
基金funded by the Science,Mathematics,And Research for Transformation(SMART)program.
文摘We study the simulation of specular reflection in a level set method implementation for wavefront propagation in high frequency acoustics using WENO spatial operators.To implement WENO efficiently andmaintain convergence rate,a rectangular grid is used over the physical space.When the physical domain does not conformto the rectangular grid,appropriate boundary conditions to represent reflection must be derived to apply at grid locations that are not coincident with the reflecting boundary.A related problem is the extraction of the normal vectors to the boundary,which are required to formulate the reflection condition.A separate level set method is applied to pre-compute the boundary normals which are then stored for use in the wavefront method.Two approaches to handling the reflection boundary condition are proposed and studied:one uses an approximation to the boundary location,and the other uses a local reflection principle.The second method is shown to produce superior results.
文摘In this paper,we investigate the dynamic process of liquid bridge formation between two parallel hydrophobic plates with hydrophilic patches,previously studied in[1].We propose a dynamic Hele-Shaw model to take advantage of the small aspect ratio between the gap width and the plate size.A constrained level set method is applied to solve the model equations numerically,where a global constraint is imposed in the evolution[2]stage together with local constraints in the reinitialization[3]stage of level set function in order to limit numerical mass loss.In contrast to the finite element method used in[2],we use a finite difference method with a 5th order HJWENO scheme for spatial discretization.To illustrate the effectiveness of the constrained method,we have compared the results obtained by the standard level set method with those from the constrained version.Our results show that the constrained level set method produces physically reasonable results while that of the standard method is less reliable.Our numerical results also show that the dynamic nature of the flow plays an important role in the process of liquid bridge formation and criteria based on static energy minimization approach has limited applicability.
