高阶能量耗散ALE-SAV有限元方法用于两相Navier--Stokes流
High-order energy diminishing ALE-SAV finite element methods for two-phase Navier--Stokes flow
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中文总结 AI 辅助
提出一种满足离散能量耗散律的高阶线性ALE-SAV有限元方法，用于尖锐界面两相Navier--Stokes流，通过SAV重构和能量稳定ALE传递算子实现稳定，数值实验验证了时间二阶和空间任意高阶收敛性。
中文摘要 AI 辅助
我们针对尖锐界面两相Navier--Stokes流发展了一种满足离散能量耗散律的高阶全离散ALE-SAV有限元方法。我们引入SAV重构以确保表面能和重力势能的稳定处理，同时采用能量稳定的ALE传递算子来控制移动网格上的密度加权动能。所得格式是线性的，并满足修正的能量耗散不等式。数值实验（包括上升气泡基准测试）证明了该方法的鲁棒性，并确认了时间上的二阶收敛性和空间上的任意高阶收敛性。
英文摘要
We develop a high-order fully discrete ALE-SAV finite element method for sharp-interface two-phase Navier--Stokes flow that satisfies a discrete energy dissipation law. We introduce an SAV reformulation to ensure the stable treatment of the surface and gravitational potential energies, together with an energy-stable ALE transfer operator that controls the density-weighted kinetic energy across moving meshes. The resulting scheme is linear and satisfies a modified energy-dissipation inequality. Numerical experiments, including rising-bubble benchmarks, demonstrate the robustness of the method and confirm second-order convergence in time and arbitrarily high-order convergence in space.
发表机构
- Hong Kong Baptist University（香港浸会大学）
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