arXiv subjects

Xinhui Wang

Publications and source records attributed to Xinhui Wang.

3 recordsLinked to original sources

arXiv2026

Novel linear, decoupled, and energy dissipative schemes for the Navier-Stokes-Darcy model and extension to related two-phase flow

We construct efficient original-energy-dissipative schemes for the Navier-Stokes-Darcy model and related two-phase flows using a prediction-correction framework. A new relaxation technique is incorporated in the correction step to guarantee dissipation of the original energy, thereby ensuring unconditional boundedness of the numerical solutions for velocity and hydraulic head in the $l^{\infty}(L^2)$ and $l^2(H^1)$ norms. At each time step, the schemes require solving only a sequence of linear equations with constant coefficients. We rigorously prove that the schemes dissipate the original energy and, as an example, carry out a rigorous error analysis of the first-order scheme for the Navier-Stokes-Darcy model. Finally, a series of benchmark numerical experiments are conducted to demonstrate the accuracy, stability, and effectiveness of the proposed methods.

math.NA↗

arXiv2024

A class of new linear, efficient and high-order implicit-explicit methods for the coupled free flow-porous media system based on nonlinear Lions interface condition

In this paper, we construct and analyze new first- and second-order implicit-explicit (IMEX) schemes for the unsteady Navier-Stokes-Darcy model to describe the coupled free flow-porous media system, which is based on the scalar auxiliary variable (SAV) approach in time and finite element method in space. The constructed schemes are linear, only require solving a sequence of linear differential equations with constant coefficients at each time step, and can decouple the Navier-Stokes and Darcy systems. The unconditional stability of both the first- and second-order IMEX schemes can be derived for the coupled system equipped with the Lions interface condition, where the key point is that we should construct a new trilinear form to balance the fully explicit discretizations of the nonlinear terms in the complex system. We can also establish rigorous error estimates for the velocity and hydraulic head of the first-order scheme without any time step restriction. Numerical examples are presented to validate the proposed schemes.

math.NA↗

arXiv2020

Star order automorphisms on the poset of type 1 operators

Let $\mathcal{H}$ be a complex infinite dimensional Hilbert space and $\mathcal{B}(\mathcal{H})$ the algebra of all bounded linear operators on $\mathcal H$. The star partial order is defined by $A\overset{*}{\leq}B$ if and only if $A^*A=A^*B$ and $AA^*=AB^*$ for any $A$ and $B$ in $\mathcal B(\mathcal H)$. We give a type decomposition of operators with respect to star order. For any $A\in\mathcal B(\mathcal H)$, there are unique type 1 operator $A_1 $ which is $0$ or the supremum of those rank 1 operators less than $A_1$ and type 2 operator $A_2$ which is not greater than any rank 1 operator in star order such that $A_i\overset{*}{\leq}A$$(i=1,2)$ and $A=A_1+A_2$. Moreover, we determine all automorphisms on the poset of type 1 operators. As a consequence, we characterize continuous automorphisms on $\mathcal B(\mathcal H)$.

math.FA↗