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Symmetry-preserving (mimetic) discretization aims to preserve certain properties of a continuous differential operator in its discrete counterpart. For these discretizations, stability and (discrete) conservation of mass, momentum and…

Numerical Analysis · Mathematics 2019-09-25 B. van 't Hof , M. J. Vuik

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time discontinuous Galerkin method for the solution of the two dimensional incompressible Navier-Stokes equations on staggered unstructured triangular…

Numerical Analysis · Mathematics 2014-12-04 Maurizio Tavelli , Michael Dumbser

We present a Cartesian cut-cell finite-volume method for sharp-interface two-phase diffusion problems in static geometries. The formulation follows a two-fluid approach: independent diffusion equations are discretized in each phase on a…

Numerical Analysis · Mathematics 2026-01-07 Louis Libat , Can Selçuk , Eric Chénier , Vincent Le Chenadec

This work presents a non-linear extension of the high-order discretisation framework based on the Variational Multiscale (VMS) method previously introduced for steady linear problems. We build on the concept of an optimal projector defined…

Numerical Analysis · Mathematics 2025-12-22 Suyash Shrestha , Marc Gerritsma , Gonzalo Rubio , Steven Hulshoff , Esteban Ferrer

We have developed dynamic manifold solutions for the Navier-Stokes equations using an extension of differential geometry called the calculus for moving surfaces. Specifically, we have shown that the geometric solutions to the Navier-Stokes…

Analysis of PDEs · Mathematics 2024-05-27 David V. Svintradze

We present a novel fully implicit hybrid finite volume/finite element method for incompressible flows. Following previous works on semi-implicit hybrid FV/FE schemes, the incompressible Navier-Stokes equations are split into a pressure and…

Numerical Analysis · Mathematics 2023-02-14 Alessia Lucca , Saray Busto , Michael Dumbser

Motivated by the increased interest in pulsed-power magneto-inertial fusion devices in recent years, we present a method for implementing an arbitrarily shaped embedded boundary on a Cartesian mesh while solving the equations of…

Computational Physics · Physics 2026-01-08 Samuel W. Jones , Colin P. McNally , Meritt Reynolds

We present a fully conservative, skew-symmetric finite difference scheme on transformed grids. The skew-symmetry preserves the kinetic energy by first principles, simultaneously avoiding a central instability mechanism and numerical…

Fluid Dynamics · Physics 2013-09-02 Julius Reiss , Jörn Sesterhenn

In this paper we propose a novel arbitrary high order accurate semi-implicit space-time DG method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As…

Numerical Analysis · Mathematics 2016-06-22 Maurizio Tavelli , Michael Dumbser

We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…

Numerical Analysis · Mathematics 2023-06-21 Harald Garcke , Robert Nürnberg , Quan Zhao

We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The…

Numerical Analysis · Mathematics 2020-11-26 Ingo Nitschke , Sebastian Reuther , Axel Voigt

We propose and analyze computationally a new fictitious domain method, based on higher order space-time finite element discretizations, for the simulation of the nonstationary, incompressible Navier-Stokes equations on evolving domains. The…

Numerical Analysis · Mathematics 2022-06-22 Mathias Anselmann , Markus Bause

This paper introduces a robust reformulation of the incompressible Navier-Stokes equations, establishing a foundational framework for designing efficient, structure-preserving algorithms that strictly conserve the original energy…

Numerical Analysis · Mathematics 2025-08-12 Zihan Weng , Qi Hong , Chunwu Wang , Yuezheng Gong

Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…

Fluid Dynamics · Physics 2025-04-01 Xinjie Ji , James Gabbard , Wim M. van Rees

We develop a high-fidelity numerical solver for the compressible Navier-Stokes equations, with the main aim of highlighting the predictive capabilities of low-diffusive numerics for flows in complex geometries. The space discretization of…

Fluid Dynamics · Physics 2016-12-16 Davide Modesti , Sergio Pirozzoli

We develop a Bayesian methodology for numerical solution of the incompressible Navier--Stokes equations with quantified uncertainty. The central idea is to treat discretized Navier--Stokes dynamics as a state-space model and to view…

Computation · Statistics 2026-02-04 Nicholas Polson , Vadim Sokolov

An immersed-boundary method for the incompressible Navier--Stokes equations is presented. It employs discrete forcing for a sharp discrimination of the solid-fluid interface, and achieves second-order accuracy, demonstrated in examples with…

A computationally efficient method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. The method formally discretizes the incompressible Navier-Stokes equations on an unbounded staggered…

Fluid Dynamics · Physics 2016-05-25 Sebastian Liska , Tim Colonius

We present a numerical formulation for the solution of non-isothermal, compressible, Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical…

We present a discrete exterior calculus (DEC) based discretization scheme for incompressible two-phase flows. Our physically-compatible exterior calculus discretization of single phase flow is extended to simulate immiscible two-phase flows…

Fluid Dynamics · Physics 2023-06-14 Minmiao Wang , Pankaj Jagad , Anil N. Hirani , Ravi Samtaney