ADirect-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems

In this paper,we develop a direct-forcing immersed boundary projection method for simulating the dynamics in thermal fluid-solid interaction problems.The underlying idea of the method is that we treat the solid as made of fluid and introduce two virtual forcing terms.First,a virtual fluid force distributed only on the solid region is appended to the momentum equation to make the region behave like a real solid body and satisfy the prescribed velocity.Second,a virtual heat source located inside the solid region near the boundary is added to the energy transport equation to impose the thermal boundary condition on the solid boundary.We take the implicit second-order backward differentiation to discretize the time variable and employ the Choi-Moin projection scheme to split the coupled system.As for spatial discretization,second-order centered differences over a staggered Cartesian grid are used on the entire domain.The advantages of this method are its conceptual simplicity and ease of implementation.Numerical experiments are performed to demonstrate the high performance of the proposed method.Convergence tests show that the spatial convergence rates of all unknowns seem to be super-linear in the 1-norm and 2-norm while less than linear in the maximum norm.

A High-Accuracy Finite Difference Scheme for Solving Reaction-Convection-Diffusion Problems with a Small Diffusivity

This paper is devoted to a new high-accuracy finite difference scheme for solving reaction-convection-diffusion problems with a small diffusivityε.With a novel treatment for the reaction term,we first derive a difference scheme of accuracy O(ε^(2)h+εh^(2)+h^(3))for the 1-D case.Using the alternating direction technique,we then extend the scheme to the 2-D case on a nine-point stencil.We apply the high-accuracy finite difference scheme to solve the 2-D steady incompressible Navier-Stokes equations in the stream function-vorticity formulation.Numerical examples are given to illustrate the effectiveness of the proposed difference scheme.Comparisons made with some high-order compact difference schemes show that the newly proposed scheme can achieve good accuracy with a better stability。

A Tailored Finite Point Method for Solving Steady MHD Duct Flow Problems with Boundary Layers

In this paper we propose a development of the finite difference method,called the tailored finite point method,for solving steady magnetohydrodynamic(MHD)duct flow problems with a high Hartmann number.When the Hartmann number is large,the MHD duct flow is convection-dominated and thus its solution may exhibit localized phenomena such as the boundary layer.Most conventional numerical methods can not efficiently solve the layer problem because they are lacking in either stability or accuracy.However,the proposed tailored finite point method is capable of resolving high gradients near the layer regions without refining the mesh.Firstly,we devise the tailored finite point method for the scalar inhomogeneous convectiondiffusion problem,and then extend it to the MHD duct flow which consists of a coupled system of convection-diffusion equations.For each interior grid point of a given rectangular mesh,we construct a finite-point difference operator at that point with some nearby grid points,where the coefficients of the difference operator are tailored to some particular properties of the problem.Numerical examples are provided to show the high performance of the proposed method.

Advection-Enhanced Gradient Vector Flow for Active-Contour Image Segmentation

In this paper,we propose a new gradient vector flow model with advection enhancement,called advection-enhanced gradient vector flow,for calculating the external force employed in the active-contour image segmentation.The proposed model is mainly inspired by the functional derivative of an adaptive total variation regularizer whose minimizer is expected to be able to effectively preserve the desired object boundary.More specifically,by incorporating an additional advection term into the usual gradient vector flow model,the resulting external force can much better help the active contour to recover missing edges,to converge to a narrow and deep concavity,and to preserve weak edges.Numerical experiments are performed to demonstrate the high performance of the newly proposed model.