Related papers: Entropy stable spectral collocation schemes for th…
We present a provably stable discontinuous Galerkin spectral element method for the incompressible Navier-Stokes equations with artificial compressibility and variable density. Stability proofs, which include boundary conditions, that…
In this paper, we present consistent and inconsistent discontinuous Galerkin methods for incompressible Euler and Navier-Stokes equations with the kinematic pressure, Bernoulli function and EMAC function. Semi- and fully discrete energy…
The anelastic and pseudo-incompressible equations are two well-known soundproof approximations of compressible flows useful for both theoretical and numerical analysis in meteorology, atmospheric science, and ocean studies. In this paper,…
In this paper, we study the dynamic stability of the 3D axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional (1D) model which approximates the Navier-Stokes equations along the symmetry axis. An…
In this paper, we design a novel class of arbitrarily high-order structure-preserving numerical schemes for the time-dependent Gross-Pitaevskii equation with angular momentum rotation in three dimensions. Based on the idea of the scalar…
Obtaining reliable numerical simulations of turbulent fluids is a challenging problem in computational fluid mechanics. The Large Eddy Simulations (LES) models are efficient tools to approximate turbulent fluids and an important step in the…
The treatment of complex geometries in Computational Fluid Dynamics applications is a challenging endeavor, which immersed boundary and cut-cell techniques can significantly simplify by alleviating the meshing process required by…
We study the construction of subgrid-scale models for large-eddy simulation of incompressible turbulent flows. In particular, we aim to consolidate a systematic approach of constructing subgrid-scale models, based on the idea that it is…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
We develop an enriched Galerkin (EG) method for the incompressible Navier-Stokes equations that conserves both kinetic energy and helicity in the inviscid limit without introducing any additional projection variables. The method employs an…
Entropy conservation and stability of numerical methods in gas dynamics have received much interest. Entropy conservative numerical fluxes can be used as ingredients in two kinds of schemes: Firstly, as building blocks in the subcell flux…
Provable nonlinear stability bounds the discrete approximation and ensures that the discretization does not diverge. For high-order methods, discrete nonlinear stability and entropy stability, have been successfully implemented for…
This paper introduces a family of entropy-conserving finite-difference discretizations for the compressible flow equations. In addition to conserving the primary quantities of mass, momentum, and total energy, the methods also preserve…
This study proposes an extension of the high-order compact gas-kinetic scheme (CGKS) to compressible flow simulation in an arbitrary Lagrangian-Eulerian (ALE) formulation in unstructured mesh. The ALE method is achieved by subdividing…
This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…
The paper introduces a geometrically unfitted finite element method for the numerical solution of the tangential Navier--Stokes equations posed on a passively evolving smooth closed surface embedded in $\mathbb{R}^3$. The discrete…
We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may…
Many entropy-conservative and entropy-stable (summarized as entropy-preserving) methods for hyperbolic conservation laws rely on Tadmor's theory for two-point entropy-preserving numerical fluxes and its higher-order extension via flux…
In this work we adapt classical residual-based stabilization techniques to the spline collocation setting. Inspired by the Streamline-Upwind-Petrov-Galerkin and Pressure-Stabilizing-Petrov-Galerkin methods, our stabilized collocation…
In this paper, we describe a new hydrodynamics code for 1D and 2D astrophysical simulations, BETHE-hydro, that uses time-dependent, arbitrary, unstructured grids. The core of the hydrodynamics algorithm is an arbitrary Lagrangian-Eulerian…