Optimized Runge-Kutta methods with automatic step size control for compressible computational fluid dynamics
DOI10.1007/s42967-021-00159-wOpenAlexW3217249011MaRDI QIDQ2084906
Hendrik Ranocha, David I. Ketcheson, Matteo Parsani, Lisandro D. Dalcín
Publication date: 13 October 2022
Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2104.06836
compressible Navier-Stokes equationsstep size controlexplicit Runge-Kutta methodscompressible Euler equations\(hp\)-adaptive spatial discretizations
Spectral methods applied to problems in fluid mechanics (76M22) Finite element methods applied to problems in fluid mechanics (76M10) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Initial-boundary value problems for first-order hyperbolic systems (35L50) Compressible fluids and gas dynamics (76N99) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)
Related Items (1)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domains
- Entropy stable discontinuous interfaces coupling for the three-dimensional compressible Navier-Stokes equations
- Entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations
- A new class of high-order energy stable flux reconstruction schemes
- Runge-Kutta pairs of order \(5(4)\) satisfying only the first column simplifying assumption
- Runge-Kutta methods with minimum storage implementations
- Embedded Runge-Kutta formulae with stable equilibrium states
- A 3(2) pair of Runge-Kutta formulas
- Time step restrictions for Runge-Kutta discontinuous Galerkin methods on triangular grids
- A PI stepsize control for the numerical solution of ordinary differential equations
- Efficient implementation of essentially nonoscillatory shock-capturing schemes
- A family of embedded Runge-Kutta formulae
- High order embedded Runge-Kutta formulae
- Contractivity of Runge-Kutta methods
- Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations
- High order entropy conservative central schemes for wide ranges of compressible gas dynamics and MHD flows
- Energy stable and high-order-accurate finite difference methods on staggered grids
- An efficient Runge-Kutta \((4,5)\) pair
- Additive Runge-Kutta schemes for convection-diffusion-reaction equations
- Automatic control and adaptive time-stepping
- Optimal stability polynomials for numerical integration of initial value problems
- Elastic wave propagation in anisotropic solids using energy-stable finite differences with weakly enforced boundary and interface conditions
- High-order accurate entropy-stable discontinuous collocated Galerkin methods with the summation-by-parts property for compressible CFD frameworks: scalable SSDC algorithms and flow solver
- On the robustness and performance of entropy stable collocated discontinuous Galerkin methods
- Embedded pairs for optimal explicit strong stability preserving Runge-Kutta methods
- Optimized explicit Runge-Kutta schemes for high-order collocated discontinuous Galerkin methods for compressible fluid dynamics
- Fully discrete explicit locally entropy-stable schemes for the compressible Euler and Navier-Stokes equations
- Entropy stable \(h/p\)-nonconforming discretization with the summation-by-parts property for the compressible Euler and Navier-Stokes equations
- General relaxation methods for initial-value problems with application to multistep schemes
- Local error estimation and step size control in adaptive linear multistep methods
- Efficient two-step Runge-Kutta methods for fluid dynamics simulations
- Optimal explicit Runge-Kutta methods for compressible Navier-Stokes equations
- Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations
- Time-step selection algorithms: adaptivity, control, and signal processing
- Adaptive time-stepping and computational stability
- Entropy Stable Spectral Collocation Schemes for the Navier--Stokes Equations: Discontinuous Interfaces
- Julia: A Fresh Approach to Numerical Computing
- Implementing Spectral Methods for Partial Differential Equations
- Analysis of Stepsize Selection Schemes for Runge-Kutta Codes
- Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods
- Temporal Error Control for Convection-Dominated Equations in Two Space Dimensions
- An Assessment of the Efficiency of Nodal Discontinuous Galerkin Spectral Element Methods
- Solving Ordinary Differential Equations II
- Relaxation Runge--Kutta Methods: Conservation and Stability for Inner-Product Norms
- Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations
- Efficient Entropy Stable Gauss Collocation Methods
- Optimized Explicit Runge--Kutta Schemes for the Spectral Difference Method Applied to Wave Propagation Problems
- Highly Efficient Strong Stability-Preserving Runge–Kutta Methods with Low-Storage Implementations
- Digital filters in adaptive time-stepping
- Numerical Methods for Ordinary Differential Equations
- A wave propagation method for three-dimensional hyperbolic conservation laws
This page was built for publication: Optimized Runge-Kutta methods with automatic step size control for compressible computational fluid dynamics
