Godunov-type schemes

E173919

finite-volume method method for hyperbolic conservation laws numerical method shock-capturing scheme

Godunov-type schemes are a class of finite-volume numerical methods for solving hyperbolic conservation laws that use Riemann solvers to accurately capture shock waves and discontinuities.

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All labels observed (13)

Label	Occurrences
Godunov's scheme	2
A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics	1
Godounov	1
Godunov's method for hyperbolic conservation laws	1
Godunov's scheme for solving hyperbolic conservation laws	1
Godunov's theorem in numerical analysis	1
Godunov-type finite volume schemes	1
Godunov-type methods	1
Godunov-type schemes canonical	1
HLL Riemann solver	1
Osher–Chakravarthy schemes	1
Osher–Solomon schemes	1
WENO schemes	1

How this entity was disambiguated

This entity first appeared as the object of triple T1523248 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Godunov-type schemes
Context triple: [Euler equations, solvedBy, Godunov-type schemes]

A. Crank–Nicolson scheme
The Crank–Nicolson scheme is a finite difference method for numerically solving time-dependent partial differential equations, especially parabolic ones like the heat equation, known for its second-order accuracy and unconditional stability.
B. Courant–Friedrichs–Lewy condition
The Courant–Friedrichs–Lewy condition is a fundamental stability criterion in numerical analysis that restricts the time step size in discretized partial differential equations to ensure convergence of the computed solution.
C. von Neumann stability analysis
Von Neumann stability analysis is a mathematical technique used in numerical analysis to determine the stability of finite difference schemes for solving partial differential equations by examining the growth of Fourier modes.
D. Lax equivalence theorem
The Lax equivalence theorem is a fundamental result in numerical analysis stating that for a well-posed linear initial value problem, consistency and stability of a finite difference scheme together imply its convergence.
E. Successive Over-Relaxation
Successive Over-Relaxation is an iterative numerical method that accelerates the convergence of the Gauss–Seidel algorithm for solving large systems of linear equations by introducing a relaxation factor.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Godunov-type schemes
Target entity description: Godunov-type schemes are a class of finite-volume numerical methods for solving hyperbolic conservation laws that use Riemann solvers to accurately capture shock waves and discontinuities.

A. Crank–Nicolson scheme
The Crank–Nicolson scheme is a finite difference method for numerically solving time-dependent partial differential equations, especially parabolic ones like the heat equation, known for its second-order accuracy and unconditional stability.
B. Courant–Friedrichs–Lewy condition
The Courant–Friedrichs–Lewy condition is a fundamental stability criterion in numerical analysis that restricts the time step size in discretized partial differential equations to ensure convergence of the computed solution.
C. von Neumann stability analysis
Von Neumann stability analysis is a mathematical technique used in numerical analysis to determine the stability of finite difference schemes for solving partial differential equations by examining the growth of Fourier modes.
D. Lax equivalence theorem
The Lax equivalence theorem is a fundamental result in numerical analysis stating that for a well-posed linear initial value problem, consistency and stability of a finite difference scheme together imply its convergence.
E. Successive Over-Relaxation
Successive Over-Relaxation is an iterative numerical method that accelerates the convergence of the Gauss–Seidel algorithm for solving large systems of linear equations by introducing a relaxation factor.
F. None of above. chosen

Statements (48)

Predicate	Object
instanceOf	finite-volume method ⓘ method for hyperbolic conservation laws ⓘ numerical method ⓘ shock-capturing scheme ⓘ
advantage	accurate resolution of shocks without artificial viscosity ⓘ
aimTo	avoid spurious oscillations near discontinuities ⓘ preserve conservation at the discrete level ⓘ
basedOn	Godunov's method ⓘ
canBe	first-order accurate ⓘ high-order accurate ⓘ second-order accurate ⓘ
contrastWith	artificial-viscosity methods ⓘ central-difference schemes ⓘ
designedFor	capturing contact discontinuities ⓘ capturing rarefaction waves ⓘ capturing shock waves ⓘ
include	ENO schemes ⓘ Godunov's first-order scheme ⓘ MUSCL schemes ⓘ TVD schemes ⓘ WENO schemes ⓘ
introducedInContextOf	compressible Euler equations ⓘ
keyIdea	conservative discretization of fluxes ⓘ solve local Riemann problems at cell interfaces ⓘ update cell averages using numerical fluxes ⓘ
namedAfter	Sergei K. Godunov ⓘ
property	conservative ⓘ shock-capturing ⓘ upwind ⓘ well-suited for discontinuous solutions ⓘ
require	Courant–Friedrichs–Lewy condition ⓘ
solve	hyperbolic conservation laws ⓘ systems of conservation laws ⓘ
timeIntegration	Runge–Kutta methods ⓘ explicit time-stepping ⓘ
typicalDomain	astrophysical fluid dynamics ⓘ computational fluid dynamics ⓘ gas dynamics ⓘ magnetohydrodynamics ⓘ
typicalGrid	structured grids ⓘ unstructured grids ⓘ
use	Riemann solvers ⓘ approximate Riemann solvers ⓘ cell-averaged conserved variables ⓘ exact Riemann solvers ⓘ finite-volume discretization ⓘ flux limiters ⓘ slope limiters ⓘ

How these facts were elicited