Related papers: Positivity-Preserving Entropy-Based Adaptive Filte…
A class of high-order lowpass filters, the discrete singular convolution (DSC) filters, is utilized to facilitate the Fourier pseudospectral method for the solution of hyperbolic conservation law systems. The DSC filters are implemented…
In this work, a novel artificial viscosity method is proposed using smooth and compactly supported viscosities. These are derived by revisiting the widely used piecewise constant artificial viscosity method of Persson and Peraire as well as…
A hydraulic fracturing system with super-hydrophobic proppants is characterized by a transient triple-porosity Navier-Stokes model. For this complex multiphysics system, particularly in the context of three-dimensional space, a local…
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 work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it…
In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite…
In this work we construct reliable a posteriori estimates for some discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together…
In this paper we study structure-preserving numerical methods for low Mach number barotropic Euler equations. Besides their asymptotic preserving properties that are crucial in order to obtain uniformly consistent and stable approximations…
Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is…
In this paper, we extend the positivity-preserving, entropy stable first-order finite volume-type scheme developed for the one-dimensional compressible Navier-Stokes equations in [1] to three spatial dimensions. The new first-order scheme…
We present a stable spectral vanishing viscosity for discontinuous Galerkin schemes, with applications to turbulent and supersonic flows. The idea behind the SVV is to spatially filter the dissipative fluxes, such that it concentrates in…
We adapt the spectral viscosity (SV) formulation implemented as a modal filter to a Spectral Difference Method (SD) solving hyperbolic conservation laws. In the SD Method we use selections of different orthogonal polynomials (APK…
This work concerns the numerical approximation of a multicomponent compressible Euler system for a fluid mixture in multiple space dimensions on unstructured meshes with a high-order discontinuous Galerkin spectral element method (DGSEM).…
A systematic analysis of the discrete conservation properties of non-dissipative, central-difference approximations of the compressible Navier-Stokes equations is reported. A general triple splitting of the nonlinear convective terms is…
We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on a monolithic convex limiting approach and prove a…
Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion…
Enhanced local-excitation retention in atomic arrays allows to exploit cooperative radiative effects to suppress emission and prolong excited-state lifetimes. We consider an impurity-assisted setting involving a single storage atom being…
The algebraic flux correction (AFC) schemes presented in this work constrain a standard continuous finite element discretization of a nonlinear hyperbolic problem to satisfy relevant maximum principles and entropy stability conditions. The…
We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties allow for accurate computations of stationary states and long-time asymptotics…
A novel approach for the stabilization of the Spectral-Volume (SV) method based on Dafermos' entropy rate criterion is presented. The method is an adaption of an already existing approach for the stabilization of the Discontinuous-Galerkin…