fluid simulation fundamentals

laval

Before simulating a lava lamp, learn how a computer represents a fluid. A sustained thermal flow needs an energy source and an energy sink. The heater adds temperature while ambient cooling continuously removes it.

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Click a cell to inspect its coordinates.

—selected cell

—array index

—cell value

0update steps

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section 1

A fluid needs an address

We divide a rectangular region into cells. Each cell has an x and y coordinate, just like a pixel.

neighbor blend per step25%

Each cell closes this percentage of the difference between itself and its neighbors.

distance per step0.75 cells

How far backward each cell looks along its velocity vector.

pressure iterations60

More iterations approximate the pressure solution more closely.

mean |divergence|: —

wall leakage

outward-pointing wall cells: —

buoyancy strength0.50

How much upward velocity one step adds in hotter cells.

heater per step0.12cooling per step2%

The heater adds temperature at the bottom; cooling removes this fraction from every cell.

temperature diffusion15%wall cooling8%

Conduction exchanges heat with neighbors; wall cooling removes heat only at the glass boundary.

neutral temperature0.50density response1.20

Wax above neutral gets an upward push; wax below neutral gets a downward push.

melting temperature0.55transition width0.10solid drag85%

Cold wax resists velocity; hot wax becomes mobile across a smooth melting range.

interface sharpening50%

Pushes mixed wax fractions toward carrier (0) or wax (1) after advection.

latent heat coupling70%

How strongly excess heat near the melt point changes melt progress instead of temperature.

surface tension0.35

Scales the curvature force applied only near the wax–carrier interface.

carrier viscosity5%hot-wax viscosity10%cold-wax viscosity45%

Each value is the fraction of the difference toward neighboring velocity closed per step.

time per frame1.00substeps4

max travel per substep: —

lamp presetsteps per second6

wax —avg temp —melt —max speed —

heater unevenness60%

Creates deterministic hot and cool patches across the bottom heater.

neck sensitivity55%pinch strength45%

detected neck cells: 0 · wax error: 0.000

Cyan outlines show narrow bridges. Removed wax is returned to nearby thicker wax.

mass correction100%

raw drift 0.000after correction 0.000

Measures wax before the substep and returns numerical gain or loss across mixed interface cells.

energy ledger this substep

heater +0.000cooling 0.000stored latent 0.000numerical drift 0.000

Thermal energy is temperature plus energy stored in melt progress. Heating and cooling are intentional transfers; drift is not.

closed material inventory

total wax 0.0last moved 0.00

Clicking an empty cell withdraws the same wax amount from existing cells, preferring the bottom reservoir.

wax motion

height 0%rising 0%falling 0%

The blue trace is the wax center of mass. Repeated peaks and valleys indicate a circulating cycle.

wax connection threshold35%

blobs 0largest 0%split events 0merge events 0

Colored outlines identify cells belonging to the same four-neighbor connected region.

persistent identity matching

next identity 1matched 0

A region keeps its outline color when most cells overlap a region from the previous frame.

identity search radius1 cell

When direct overlap fails, search this far around the new region for its previous identity.

cycle quality

height range 0%active blobs 0

A useful lamp has a changing center height and more than one connected wax region without becoming unstable.

cell width0.5 cmseconds per frame0.10 s

reported maximum speed: 0.0 cm/s

complete model

blobs 0cycle range 0%rising 0%falling 0%

This runs the closed, mass-corrected, heated, cooled, two-phase timestep with pinch-off and persistent blob tracking.

wax particle mass220base concentration75%particle cohesion70%glass cooling10%

particles 0 · blobs 0

target neighbor density3.0volume pressure90%

maximum particle density: 0.0

const field = createScalarField(28, 18);\n\nfield.at(x, y);

What to noticeA two-dimensional cell can live in a one-dimensional array.

Deliberately not includedThere is no motion, pressure, viscosity, or fluid physics yet.

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The path from this grid to a lava lamp

checkpoint 01Grid + scalar field

02Velocity vectors

03Advection

04Diffusion

05Divergence

06Pressure projection

07Boundaries

08Heat + buoyancy

09Heat transport gap

10Coupled thermal step

11Heating + cooling

12Conduction + wall cooling

13Wax material field

14Temperature-driven density

15Phase change + solid drag

16Wax interface

17Latent heat

18Cohesion + surface tension

19Phase-dependent viscosity

20Stable complete timestep

21Continuous calibrated lamp

22Uneven heating + bottom pool

23Pinch-off + recombination

24Wax conservation

25Energy budget

26Closed vessel

27Cycle diagnostics

28Blob components

29Persistent identity

30Motion matching

31Cycle calibration

32Physical units

33Final simulator

34Shaped lamp vessel

35Particle volume pressure

Current claim: this demonstrates a grid, a scalar field, and neighbor-based smoothing. It is not yet a fluid simulation.

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fluid simulation fundamentals

laval

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Click a cell to inspect its coordinates.

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—selected cell

\\n

—array index

\\n

—cell value

\\n

0update steps

\\n

\\n\\n

\\n

section 1

\\n

A fluid needs an address

\\n

We divide a rectangular region into cells. Each cell has an x and y coordinate, just like a pixel.

\\n

neighbor blend per step25%

Each cell closes this percentage of the difference between itself and its neighbors.

\\n

distance per step0.75 cells

How far backward each cell looks along its velocity vector.

\\n

pressure iterations60

More iterations approximate the pressure solution more closely.

mean |divergence|: —

\\n

wall leakage

outward-pointing wall cells: —

\\n

buoyancy strength0.50

How much upward velocity one step adds in hotter cells.

\\n

heater per step0.12cooling per step2%

The heater adds temperature at the bottom; cooling removes this fraction from every cell.

\\n

temperature diffusion15%wall cooling8%

Conduction exchanges heat with neighbors; wall cooling removes heat only at the glass boundary.

\\n

neutral temperature0.50density response1.20

Wax above neutral gets an upward push; wax below neutral gets a downward push.

\\n

melting temperature0.55transition width0.10solid drag85%

Cold wax resists velocity; hot wax becomes mobile across a smooth melting range.

\\n

interface sharpening50%

Pushes mixed wax fractions toward carrier (0) or wax (1) after advection.

\\n

latent heat coupling70%

How strongly excess heat near the melt point changes melt progress instead of temperature.

\\n

surface tension0.35

Scales the curvature force applied only near the wax–carrier interface.

\\n

carrier viscosity5%hot-wax viscosity10%cold-wax viscosity45%

Each value is the fraction of the difference toward neighboring velocity closed per step.

\\n

time per frame1.00substeps4

max travel per substep: —

\\n

lamp presetsteps per second6

wax —avg temp —melt —max speed —

\\n

heater unevenness60%

Creates deterministic hot and cool patches across the bottom heater.

\\n

neck sensitivity55%pinch strength45%

detected neck cells: 0 · wax error: 0.000

Cyan outlines show narrow bridges. Removed wax is returned to nearby thicker wax.

\\n

mass correction100%

raw drift 0.000after correction 0.000

Measures wax before the substep and returns numerical gain or loss across mixed interface cells.

\\n

energy ledger this substep

heater +0.000cooling 0.000stored latent 0.000numerical drift 0.000

Thermal energy is temperature plus energy stored in melt progress. Heating and cooling are intentional transfers; drift is not.

\\n

closed material inventory

total wax 0.0last moved 0.00

Clicking an empty cell withdraws the same wax amount from existing cells, preferring the bottom reservoir.

\\n

wax motion

height 0%rising 0%falling 0%

The blue trace is the wax center of mass. Repeated peaks and valleys indicate a circulating cycle.

\\n

wax connection threshold35%

blobs 0largest 0%split events 0merge events 0

Colored outlines identify cells belonging to the same four-neighbor connected region.

\\n

persistent identity matching

next identity 1matched 0

A region keeps its outline color when most cells overlap a region from the previous frame.

\\n

identity search radius1 cell

When direct overlap fails, search this far around the new region for its previous identity.

\\n

cycle quality

height range 0%active blobs 0

A useful lamp has a changing center height and more than one connected wax region without becoming unstable.

\\n

cell width0.5 cmseconds per frame0.10 s

reported maximum speed: 0.0 cm/s

\\n

complete model

blobs 0cycle range 0%rising 0%falling 0%

This runs the closed, mass-corrected, heated, cooled, two-phase timestep with pinch-off and persistent blob tracking.

\\n

wax particle mass220base concentration75%particle cohesion70%glass cooling10%

particles 0 · blobs 0

\\n

target neighbor density3.0volume pressure90%

maximum particle density: 0.0

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const field = createScalarField(28, 18);\\n\\nfield.at(x, y);

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What to noticeA two-dimensional cell can live in a one-dimensional array.

\\n

Deliberately not includedThere is no motion, pressure, viscosity, or fluid physics yet.

\\n

\\n\\n

\\n

The path from this grid to a lava lamp

\\n

checkpoint 01Grid + scalar field

\\n

02Velocity vectors

\\n

03Advection

\\n

04Diffusion

\\n

05Divergence

\\n

06Pressure projection

\\n

07Boundaries

\\n

08Heat + buoyancy

\\n

09Heat transport gap

\\n

10Coupled thermal step

\\n

11Heating + cooling

\\n

12Conduction + wall cooling

\\n

13Wax material field

\\n

14Temperature-driven density

\\n

15Phase change + solid drag

\\n

16Wax interface

\\n

17Latent heat

\\n

18Cohesion + surface tension

\\n

19Phase-dependent viscosity

\\n

20Stable complete timestep

\\n

21Continuous calibrated lamp

\\n

22Uneven heating + bottom pool

\\n

23Pinch-off + recombination

\\n

24Wax conservation

\\n

25Energy budget

\\n

26Closed vessel

\\n

27Cycle diagnostics

\\n

28Blob components

\\n

29Persistent identity

\\n

30Motion matching

\\n

31Cycle calibration

\\n

32Physical units

\\n

33Final simulator

\\n

34Shaped lamp vessel

\\n

35Particle volume pressure

\\n

Current claim: this demonstrates a grid, a scalar field, and neighbor-based smoothing. It is not yet a fluid simulation.

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Diff · v239