Oct 2025· Journal of Scientific Computing· Vol 109· 0 citations· 46 references
Computer ScienceMathematics
Abstract
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 discontinuous Galerkin discretization that is mass-conservative, energy-stable, and provides arbitrary-order accuracy in space and second-order accuracy in time. The approach relies on the approach in [21] and a special splitting discretization of the derivatives of the free energy function within the Crank-Nicolson time-stepping. Numerical experiments confirm the analytical statements and show the applicability of the approach.
This paper is devoted to the analysis of the global well-posedness of strong solutions to a coupled system consisting of the thermomechanical Cucker–Smale model and the incompressible Navier–Stokes equations (TCS–NS) in R2. Employing an iterative construction, we first establish the local existence and uniqueness of st...
Yang Bai, L. Zeng, Wei-Yuan Zou· Journal of Mathematics and P...· 0 citations
We present an energy-stable discontinuous Galerkin (DG) spatial discretization of the intrinsic beam equations with Kelvin-Voigt damping. We reformulate the governing equations by splitting the total sectional resultants into elastic and viscous parts, thereby exposing a mixed system without mixed space-time derivative...
Shivam Sundriyal, Christian Bleffert, Lukas Dreyer et al.· 0 citations
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 AL...
In this paper, we propose a grad-div stabilization and rotational pressure-correction (GSRP) method with second-order temporal discretization for solving the unsteady incompressible thermosolutal convection coupled with magnetohydrodynamics (UITC-MHD) system. The method simultaneously enhances computational accuracy an...
You-Lei Liang, Lun-Ji Song· International Journal of Num...· 0 citations
We develop structure-preserving methods for the compressible Euler equations with gravity in vector-invariant form and potential temperature as a prognostic variable within the flux-differencing discontinuous Galerkin spectral element method (DGSEM) framework. By discretizing the nonconservative terms as symmetric and...
Marco Artiano, Kieran Ricardo, O. Knoth et al.· 0 citations
For any nontrivial divergence‐free initial data in H12$H^\frac{1}{2}$ , we prove the existence of infinitely many dissipative solutions to both the 3D Navier–Stokes and MHD equations, whose energy profiles are continuous and decreasing on [0,∞)$[0,\infty)$ . If the initial data is only L2$L^2$ , our construction yields...
Alexey Cheskidov, Zi-Rong Zeng, Deng Zhang· Proceedings of the London Ma...· 0 citations
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