Adaptive mesh refinement · multiresolution

Finite-volume simulations that refine themselves.

A community catalogue of simulation cases built with samurai. Each entry is reproducible from a single folder: the code, the equations, and the run that produced the image.

14 cases
Method
Dim
Mesh
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Linear advection of a disc
Fig. 01 Finite volume · 2D

Linear advection of a disc

A disc is transported diagonally while the multiresolution mesh tracks its edges.

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2D Riemann problem (config 3)
Fig. 02 Finite volume · 2D

2D Riemann problem (config 3)

Four constant states meet at a point and interact through shocks, contacts and a rolled-up jet.

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Kelvin-Helmholtz instability
Fig. 03 Finite volume · 2D

Kelvin-Helmholtz instability

Two shear layers roll up into the iconic billows; the mesh tracks the growing vortices.

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Sedov blast wave
Fig. 04 Finite volume · 2D

Sedov blast wave

A point energy release drives a circular blast wave; the mesh refines on the expanding shock.

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Level-set in a vortex flow
Fig. 05 Finite volume · 2D

Level-set in a vortex flow

A circular interface is stretched into a filament by a swirling flow, tracked by the adaptive mesh.

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2D Riemann problem (config 12)
Fig. 06 Finite volume · 2D

2D Riemann problem (config 12)

Four constant states interact through shocks and contacts (configuration 12).

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2D Riemann problem (config 4)
Fig. 07 Finite volume · 2D

2D Riemann problem (config 4)

Four constant states interact through shocks and contacts (configuration 4).

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Burgers equation (1D)
Fig. 08 Finite volume · 1D

Burgers equation (1D)

A smooth hat steepens into a shock; the multiresolution mesh follows the front.

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Burgers equation (2D)
Fig. 09 Finite volume · 2D

Burgers equation (2D)

A radial hat steepens into nonlinear fronts, tracked by the multiresolution mesh.

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Double Mach reflection
Fig. 10 Finite volume · 2D

Double Mach reflection

A Mach-10 shock strikes a wedge, producing the classic double Mach reflection pattern.

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Isentropic vortex
Fig. 11 Finite volume · 2D

Isentropic vortex

A smooth isentropic vortex advects across the domain; an exact-solution benchmark.

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Sod shock tube
Fig. 12 Finite volume · 2D

Sod shock tube

The reference Sod shock tube (rotated into 2D): rarefaction, contact and shock.

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Two-scale isothermal atomization
Fig. 13 Finite volume · 2D

Two-scale isothermal atomization

An air jet shears a liquid column that atomizes, with inter-scale mass transfer feeding a disperse phase.

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Linear convection around an obstacle
Fig. 14 Finite volume · 2D

Linear convection around an obstacle

A square profile is carried diagonally past a solid obstacle, tracked by an adaptive mesh.