arXiv subjects

Chunwu Wang

Publications and source records attributed to Chunwu Wang.

3 recordsLinked to original sources

arXiv2025

Original-energy-dissipation-preserving methods for the incompressible Navier-Stokes equations

This paper introduces a robust reformulation of the incompressible Navier-Stokes equations, establishing a foundational framework for designing efficient, structure-preserving algorithms that strictly conserve the original energy dissipation law. By leveraging Crank-Nicolson schemes and backward differentiation formulas, we develop four first- and second-order time-discrete schemes. These schemes exactly preserve the original energy dissipation law at each time step, requiring only the solutions of three linear Stokes systems and one $2\times 2$ system of linear equations. Furthermore, the finite difference approximation on a staggered grid is employed for these time-discrete systems to derive fully discrete structure-preserving schemes. We rigorously prove that all proposed fully discrete methods both maintain the original energy dissipation law and admit unique solutions. Moreover, we present their efficient implementation. Extensive numerical experiments are carried out to verify the accuracy, efficacy, and advantageous performance of our newly developed methods.

math.NA↗

arXiv2025

A high-order Newton multigrid method with a simplified Jacobian for steady-state shallow water equations

A high-order Newton multigrid method is proposed for steady-state shallow water flows in open channels with regular and irregular geometries. The method integrates a finite volume discretization with third-order weighted essentially non-oscillatory (WENO) reconstruction and a Newton multigrid framework with an efficient approximation of the Jacobian matrix for solving the resulting discrete system. In high-order schemes, the computational cost of Jacobian construction becomes dominant due to the wide stencil. Meanwhile, only a small fraction of the non-zero Jacobian entries exhibit large magnitudes. Based on this observation, a simplified Jacobian approximation is introduced using reduced stencils, in which selected off-stencil contributions are neglected, thereby achieving a substantial reduction in computational cost. The proposed approach is verified numerically to show significant efficiency improvement while maintaining comparable convergence behavior to that obtained with the full Jacobian approach. To further enhance performance, a geometric multigrid method incorporating a successive over-relaxation iteration as the smoother is applied to solve the linear systems arising in each Newton step. A variety of numerical experiments, including a one-dimensional smooth subcritical flow, flows over a hump, and a two-dimensional hydraulic jump over a wedge, are carried out to illustrate the third-order accuracy, efficiency, and robustness of the proposed method.

math.NA↗

arXiv2024

A novel fast iterative moment method for near-continuum flows

We develop a novel fast iterative moment method for the steady-state simulation of near-continuum flows, which are modeled by the high-order moment system derived from the Boltzmann-BGK equation. The fast convergence of the present method is mainly achieved by alternately solving the moment system and the hydrodynamic equations with consistent constitutive relations and boundary conditions. To be specific, the consistent hydrodynamic equations are solved in each alternating iteration to obtain improved predictions of macroscopic quantities, which are subsequently utilized to expedite the evolution of the moment system. Additionally, a semi-implicit scheme treating the collision term implicitly is introduced for the moment system. The resulting alternating iteration can be further accelerated by employing the Gauss-Seidel method with a cell-by-cell sweeping strategy. It is also noteworthy that such an alternating iteration works well with the nonlinear multigrid method. Numerical experiments for planar Couette flow, shock structure, and lid-driven cavity flow are carried out to investigate the performance of the proposed fast iterative moment method. All results show impressive efficiency and robustness.

math.NA↗