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.
A second-order exponential low-regularity integrator is proposed for the incompressible Navier--Stokes equations. The method requires only linear solves and satisfies a discrete energy-decay property. Second-order temporal convergence is established under a uniform $H^4$ solution bound, with an error constant that rema...
We consider a Navier–Stokes–Allen–Cahn (NSAC) system that governs the compressible motion of a viscous, immiscible two-phase fluid at constant temperature. Weak solutions of the NSAC system dissipate an appropriate energy functional. Based on an equivalent re-formulation of the NSAC system we propose a fully-discrete d...
L. Ostrowski, Christian Rohde· Journal of Scientific Comput...· 0 citations
In this paper, an arbitrary Lagrangian-Eulerian (ALE)-based finite element method (FEM) is developed and studied in a monolithic framework for a class of two-phase Stokes flow problems with moving interfaces and jump coefficients, where the mixed finite element approximation to Stokes moving interface problems is estab...
Yi-Teng Liang, Cheng Wang, Peng-Tao Sun et al.· 0 citations
A high-order compact modified Crank-Nicolson scheme is proposed for the nonlinear Sobolev equation, in which a convex energy splitting approach is employed to address key computational challenges. By decomposing the energy functional into two convex components, a spatially fourth-order and temporally second-order compa...
Meng-Ling Wu, Xian-Yue Li, Ke-Jia Pan et al.· Numerical Mathematics: Theor...· 0 citations
The six-equation, single-velocity, two-phase flow model based on the diffuse-interface method (DIM) with stiff pressure relaxation has recently gained attention for its ability to handle metastable fluids, ensure robust positivity of volume fractions, and yield effective sound speeds consistent with Wood’s law. However...
Qi-Chao Li, Lin Fu (Associate Professor)· Journal of Scientific Comput...· 0 citations
We present an energy bounded initial boundary value problem (IBVP) for incompressible multi-phase flows that separately conserves mass and kinetic energy. The IBVP combine perfectly with Summation-By-Parts (SBP) operators and weak boundary conditions on Simultaneous Approximation Term (SAT) form and lead to discrete ene...
J. Nordström, H. Collis, R. Brown et al.· Journal of Computational Phy...· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
