Mathematical challenges for the theory of hyperbolic balance laws in fluid mechanics: complexity, scales, randomness
DOI10.1365/s13291-024-00290-6MaRDI QIDQ6646760
Christian Rohde, Mária Lukáčová-Medvid'ová
Publication date: 3 December 2024
Published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) (Search for Journal in Brave)
Euler equationsstochastic modellinguncertainty quantificationshock wave theorystructure/asymptotic-preserving numerics
PDEs in connection with fluid mechanics (35Q35) Shock waves and blast waves in fluid mechanics (76L05) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Basic methods in fluid mechanics (76M99)
Cites Work
- Unnamed Item
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- Perfect derivatives, conservative differences and entropy stable computation of hyperbolic conservation laws
- Dissipative continuous Euler flows
- Regularity and energy conservation for the compressible Euler equations
- Compressible fluid flow and systems of conservation laws in several space variables
- A class of uniformly dissipative symmetric hyperbolic-hyperbolic systems
- On admissibility criteria for weak solutions of the Euler equations
- The Cauchy problem for quasi-linear symmetric hyperbolic systems
- Supersonic flow and shock waves. Reprint of the ed. published by Interscience Publishers, New York
- Onsager's conjecture on the energy conservation for solutions of Euler's equation
- Statistical solutions of hyperbolic conservation laws: foundations
- Dissipative structure and entropy for hyperbolic systems of balance laws
- \(L^2\)-stability analysis of IMEX-\(( \sigma,\mu )\) DG schemes for linear advection-diffusion equations
- A posteriori subcell finite volume limiter for general \(P_NP_M\) schemes: applications from gasdynamics to relativistic magnetohydrodynamics
- Limiter-based entropy stabilization of semi-discrete and fully discrete schemes for nonlinear hyperbolic problems
- A crisis for the verification and validation of turbulence simulations
- On non-uniqueness of continuous entropy solutions to the isentropic compressible Euler equations
- Energy conservation for the compressible Euler and Navier-Stokes equations with vacuum
- A high-order stochastic Galerkin code for the compressible Euler and Navier-Stokes equations
- A hyperbolicity-preserving discontinuous stochastic Galerkin scheme for uncertain hyperbolic systems of equations
- Entropy stable space-time discontinuous Galerkin schemes with summation-by-parts property for hyperbolic conservation laws
- Convergence of discontinuous Galerkin schemes for the Euler equations via dissipative weak solutions
- From gas dynamics with large friction to gradient flows describing diffusion theories
- Uncertainty Quantification for Hyperbolic Systems of Conservation Laws
- Onsager's Conjecture for Admissible Weak Solutions
- Well-posedness of the Cauchy problem for 𝑛×𝑛 systems of conservation laws
- A variational time discretization for compressible Euler equations
- Weak-Strong Uniqueness in Fluid Dynamics
- Convex Integration Applied to the Multi-Dimensional Compressible Euler Equations
- Convergence Analysis of Grad's Hermite Expansion for Linear Kinetic Equations
- Relaxation of the Navier–Stokes–Korteweg equations for compressible two‐phase flow with phase transition
- Numerical Analysis of Compressible Fluid Flows
- A posteriori error analysis for random scalar conservation laws using the stochastic Galerkin method
- Compressible multicomponent flow in porous media with Maxwell‐Stefan diffusion
- $hp$-Multilevel Monte Carlo Methods for Uncertainty Quantification of Compressible Navier--Stokes Equations
- A Stabilized DG Cut Cell Method for Discretizing the Linear Transport Equation
- Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations
- Computing oscillatory solutions of the Euler system via 𝒦-convergence
- Kinetic models of BGK type and their numerical integration
- Global Ill‐Posedness of the Isentropic System of Gas Dynamics
- Error Estimates for Finite Volume Approximations of Classical Solutions for Nonlinear Systems of Hyperbolic Balance Laws
- A Posteriori Analysis of Fully Discrete Method of Lines Discontinuous Galerkin Schemes for Systems of Conservation Laws
- FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
- Systems of Conservation Equations with a Convex Extension
- Hyperbolic Conservation Laws in Continuum Physics
- Front tracking for hyperbolic conservation laws
- Extensions of Active Flux to arbitrary order of accuracy
- The Cartesian grid active flux method with adaptive mesh refinement
- On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions
- Strong convergence of the vorticity and conservation of the energy for the α-Euler equations
- Probabilistic descriptions of fluid flow: a survey
- Convergence and error analysis of compressible fluid flows with random data: Monte Carlo method
- A well-balanced semi-implicit IMEX finite volume scheme for ideal magnetohydrodynamics at all Mach numbers
- A Review of Cartesian Grid Active Flux Methods for Hyperbolic Conservation Laws
- Existence of energy-variational solutions to hyperbolic conservation laws
- Multiderivative time integration methods preserving nonlinear functionals via relaxation
- Multirate time-integration based on dynamic ODE partitioning through adaptively refined meshes for compressible fluid dynamics
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