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In this work, a cost-efficient space-time adaptive algorithm based on the Dual Weighted Residual (DWR) method is developed and studied for a coupled model problem of flow and convection-dominated transport. Key ingredients are a multirate…

Numerical Analysis · Mathematics 2024-07-19 Marius Paul Bruchhäuser , Markus Bause

An improved numerical solver for the unified solution of compressible and incompressible fluids involving interfaces is proposed. The present method is based on the CIP-CUP (Cubic Interpolated Propagation / Combined, Unified Procedure)…

Computational Physics · Physics 2007-05-23 Masato Ida

The linear stability analysis of the Boltzmann kinetic equation has recently garnered research interest due to its potential applications in space exploration, where rarefaction effects can render the Navier Stokes equations invalid. Since…

Computational Physics · Physics 2025-08-05 Lei Wu

Many robotic systems are underactuated, meaning not all degrees of freedom can be directly controlled due to lack of actuators, input constraints, or state-dependent actuation. This property, compounded by modeling uncertainties and…

Systems and Control · Electrical Eng. & Systems 2025-10-10 Daniel M. Cherenson , Dimitra Panagou

We investigate two common numerical techniques for integrating reversible moist processes in atmospheric flows in the context of solving the fully compressible Euler equations. The first is a one-step, coupled technique based on using…

Atmospheric and Oceanic Physics · Physics 2015-05-11 Max Duarte , Ann S. Almgren , Kaushik Balakrishnan , John B. Bell , David M. Romps

The equations of stationary compressible flows of active liquid crystals are considered in a bounded three-dimensional domain. The system consists of the stationary Navier-Stokes equations coupled with the equation of Q-tensors and the…

Analysis of PDEs · Mathematics 2022-05-03 Zhilei Liang , Apala Majumdar , Dehua Wang , Yixuan Wang

The paper is concerned with an adjoint complement to the Volume-of-Fluid (VoF) method for immiscible two-phase flows, e.g. air and water, which is widely used in marine engineering due to its computational efficiency. The particular…

Fluid Dynamics · Physics 2021-06-02 Niklas Kühl , Jörn Kröger , Martin Siebenborn , Michael Hinze , Thomas Rung

In physically inviscid fluid dynamics, "shock capturing" methods adopt either an artificial viscosity contribution or an appropriate Riemann solver algorithm. These techniques are necessary to solve the strictly hyperbolic Euler equations…

Fluid Dynamics · Physics 2015-05-18 G. Lanzafame

The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D Euler equations and the first goal of this…

Fluid Dynamics · Physics 2023-05-08 Kevin Ancourt , Jacques Peter , Olivier Atinault

Adjoint based shape optimization is a powerful technique in fluid-dynamics optimization, capable of identifying an optimal shape within only dozens of design iterations. However, when extended to rarefied gas flows, the computational cost…

Computational Physics · Physics 2025-11-25 Yanbing Zhang , Ruifeng Yuan , Lei Wu

We study single-loop gradient-flow dynamics for nested optimization, where the outer variable evolves while auxiliary variables track the inner solution map. While existing analyses typically rely on problem- and condition-specific Lyapunov…

Optimization and Control · Mathematics 2026-05-21 Hyunwoo Lee , Jeongyeol Kwon , Dohyun Kwon

We present an alternative "encapsulated" formulation of the Selective Frequency Damping method for finding unstable equilibria of dynamical systems, which is particularly useful when analysing the stability of fluid flows. The formulation…

Fluid Dynamics · Physics 2015-06-18 Bastien E. Jordi , C. J. Cotter , Spencer J. Sherwin

We consider the incompressible Navier--Stokes equations with periodic boundary conditions and time-independent forcing. For this type of flow, we derive adjoint equations whose trajectories converge asymptotically to the equilibrium and…

Fluid Dynamics · Physics 2016-04-15 Mohammad Farazmand

This paper considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible…

Optimization and Control · Mathematics 2024-08-27 Ahmed Allibhoy , Jorge Cortés

In this paper, we are concerned with the three dimensional Euler equations driven by an additive stochastic forcing. First, we construct global H\"{o}lder continuous (stationary) solutions in $C(\mathbb{R};C^{\vartheta})$ space for some…

Probability · Mathematics 2025-05-20 Lin Lü

Many interesting physical problems described by systems of hyperbolic conservation laws are stiff, and thus impose a very small time-step because of the restrictive CFL stability condition. In this case, one can exploit the superior…

Numerical Analysis · Mathematics 2025-02-17 Gabriella Puppo , Matteo Semplice , Giuseppe Visconti

A new Active Flux method for the multi-dimensional Euler equations is based on an additive operator splitting into acoustics and advection. The acoustic operator is solved in a locally linearized manner by using the exact evolution…

Numerical Analysis · Mathematics 2025-06-05 Wasilij Barsukow

In this article we examine the interaction of incompressible 2D flows with compact material boundaries. Our focus is the dynamic behavior of the circulation of velocity around boundary components and the possible exchange between flow…

Analysis of PDEs · Mathematics 2013-05-07 Dragos Iftimie , Milton Lopes Filho , Helena Nussenzveig Lopes , Franck Sueur

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…

Numerical Analysis · Mathematics 2024-12-11 Dominic Breit , Thamsanqa Castern Moyo , Philipp Öffner

We consider the non-isothermal flow of a compressible fluid through pipes. Starting from the full set of Euler equations, we propose a variational characterization of solutions that encodes the conservation of mass, energy, and entropy in a…

Numerical Analysis · Mathematics 2016-11-11 Herbert Egger