Yirang Yuan

Analysis on block-centered finite differences of numerical simulation of semiconductor device detector ☆

Abstract A finite difference scheme on block-centered method is presented on nonuniform partition to simulate numerically three-dimensional transient problems of semiconductor detector of photoconduction. Applying the method of mixed finite element, the principle of duality, the induction hypothesis, the prior error theory of differential equations and other special techniques, we give error estimates of second-order accuracy in l2-norm. The numerical simulation is super-convergent for the electric field intensity, really important in actual applications.

Mixed Volume Element-Characteristic Fractional Step Difference Method for Contamination from Nuclear Waste Disposal

A nonlinear system with boundary-initial value conditions of convection–diffusion partial differential equations is presented to describe incompressible nuclear waste disposal contamination in porous media. The flow pressure is determined by an elliptic equation, the concentrations of brine and radionuclide are formulated by convection–diffusion equations, and the transport of temperature is defined by a heat equation. The pressure appears in convection–diffusion equations and heat equation in the form of Darcy velocity and controls the physical processes. The fluid pressure and velocity are solved by the conservative mixed volume element and the computation accuracy of Darcy velocity is improved one order. A combination method of the mixed volume element and the approximation of characteristics is applied to solve the brine and heat, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computation stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. Larger time-steps along the characteristics are shown to result in smaller time-truncation errors than those resulting from standard methods. The mixed volume element method has the property of conservation on each element and it can obtain numerical solutions of the brine and adjoint vectors. The radionuclide is solved by a coupled method of characteristics and fractional step difference. The computational work is reduced greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and using the algorithm of speedup. Using numerical analysis of priori estimates of differential equations, we demonstrate an optimal second order estimate in

Mixed volume element combined with characteristic mixed finite volume element method for oil–water two phase displacement problem

l^2

Numerical method of mixed finite volume-modified upwind fractional step difference for three-dimensional semiconductor device transient behavior problems

l2 norm. Numerical data are appropriate with the scheme and it is shown that the method is a powerful tool to solve the well-known problems in porous media.

Upwind finite difference method for miscible oil and water displacement problem with moving boundary values

Abstract A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced (chemical) oil production in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l2 norm is derived. This method has been applied successfully to the numerical simulation of enhanced oil production in actual oilfields, and the simulation results are quite interesting and satisfactory.

The upwind finite difference fractional steps methods for two‐phase compressible flow in porous media

Abstract As the basic of numerical simulation of energy science, the displacement of three-dimensional oil–water two phase in porous media is discussed in this paper. For incompressible miscible displacement, the pressure is described by a flow equation in an elliptic mathematical formulation and the saturation is defined by a convection–diffusion equation. The pressure exists in the saturation equation by Darcy velocity, and controls the whole flow. We develop and improve substantially the work of Arbogast and Wheeler, then put forward a mixed volume element combined with characteristic mixed finite volume element method for two-phase displacement problem. The flow equation is discretized by the conservative mixed volume element method, which could improve the accuracy of an order for computing Darcy velocity. The saturation equation is solved by a characteristic mixed volume element method, where mixed volume element method is used to compute the diffusion term and the method of characteristics is adopted to discretize the convection term. The method of characteristics can confirm high stability of numerical simulation at the fronts, avoid numerical dispersion and nonphysical oscillation, and can adopt large time steps, obtain smaller time truncation error and improve the computation accuracy. Mixed volume element can solve the convection term, confirm conservation of mass at each element and approximate the saturation and the adjoint vector meanwhile. It is most important in numerical computation of seepage mechanics. Optimal second order estimates in L 2 norm are derived by theory and special techniques of priori estimates. Finally, numerical experiments are shown to illustrate the efficiency and practicability and to solve the international problem successfully.

The characteristic finite element alternating direction method with moving meshes for nonlinear convection‐dominated diffusion problems

A parallel algorithm is presented to solve three-dimensional slightly compressible seepage displacement where domain decomposition and characteristics-mixed finite element are combined. Decomposing the computational domain into several subdomains, we define a special function to approximate the derivative at interior boundary explicitly and obtain numerical solutions of the saturation implicitly on subdomains in parallel. The method of characteristics can confirm strong stability at the fronts, and can avoid numerical dispersion and nonphysical oscillation. It can adopt large-time step but can obtain small time truncation error. So a characteristic domain decomposition finite element scheme is put forward to compute the saturation. The flow equation is computed by the method of mixed finite element and numerical accuracy of Darcy velocity is improved one order. For a model problem we apply some techniques such as variation form, domain decomposition, the method of characteristics, the principle of energy, negative norm estimates, induction hypothesis, and the theory of priori estimates of differential equations to derive optimal error estimate in

An upwind finite volume element method based on quadrilateral meshes for nonlinear convection-diffusion problems

l^2