Related papers: Truncation Error-Based Anisotropic $p$-Adaptation …
In this work, we prove what appear to be the first Reynolds-semi-robust and pressure-robust velocity error estimates for an H(div)-conforming approximation of unsteady incompressible flows of power-law type fluids. The proposed methods…
This thesis deals with the investigation of a H(div)-conforming hybrid discontinuous Galerkin discretization for incompressible turbulent flows. The discretization method provides many physical and solving-oriented properties, which may be…
We study a low-rank iterative solver for the unsteady Navier-Stokes equations for incompressible flows with a stochastic viscosity. The equations are discretized using the stochastic Galerkin method, and we consider an all-at-once…
The truncation and approximation errors for the set of numerical solutions computed by methods based on the algorithms of different structure are calculated and analyzed for the case of the two-dimensional steady inviscid compressible flow.…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
Equilibrium or stationary solutions usually proceed through the exact balance between hyperbolic transport terms and source terms. Such equilibrium solutions are affected by truncation errors that prevent any classical numerical scheme from…
The entropy conservative, curvilinear, nonconforming, p-refinement algorithm for hyperbolic conservation laws of Del Rey Fernandez et al. (2019), is extended from the compressible Euler equations to the compressible Navier-Stokes equations.…
This paper presents a class of novel high-order fully-discrete entropy stable (ES) discontinuous Galerkin (DG) schemes with explicit time discretization. The proposed methodology exploits a critical observation from [4] that the cell…
We study the time-dependent Navier-Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion, and…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
In recent years, stochastic effects have become increasingly relevant for describing fluid behaviour, particularly in the context of turbulence. The most important model for inviscid fluids in computational fluid dynamics are the Euler…
Accurate and efficient simulation of fluid-structure interaction (FSI) problems remains a central challenge in computational physics. High-order discontinuous Galerkin (DG) methods offer low numerical errors and excellent scalability on…
Multiscale mathematical models have shown great promise in computational brain electrophysiology but are still hindered by high computational costs due to fast dynamics and complex brain geometries, requiring very fine spatio-temporal…
A data-driven closure modeling based on proper orthogonal decomposition (POD) temporal modes is used to obtain stable and accurate reduced order models (ROMs) of unsteady compressible flows. Model reduction is obtained via Galerkin and…
Split form schemes for Euler and Navier-Stokes equations are useful for computation of turbulent flows due to their better robustness. This is because they satisfy additional conservation properties of the governing equations like kinetic…
This paper introduces a high order numerical framework for efficient and robust simulation of compressible flows. To address the inefficiencies of standard hybridized discontinuous Galerkin (HDG) methods in large scale settings, we develop…
This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational…
In the finite element analysis with fast decoupled time integration scheme for viscoelastic fluid (the Leonov model) flow, we investigate strong nonlinear behavior in 2D creeping contraction flow. The algorithm is applicable in the whole…
In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…
In this paper, we introduce and analyze a space-time $p$-adaptive discontinuous Galerkin method for nonlinear acoustics. We first present the underlying mathematical model, which is based on a recently derived formulation involving, in…