1D Height Field Fluid

This is a 1D implementaion of Matthias Müllers Height Field Fluid algorithm presented at the Games Developers Conference 2008. It is based on the 2D wave equation $$ u_{tt}=c^2\nabla^2u $$ in form of a partial differential equation of second order. $ u_{tt}=c^2u_{xx} $ for the 1D case.
In short, the algorithm steps are based on particle calculations in respect to Newtons second law of motion $ a=f/m $

                
                    LOOP
                        compute force
                        velocity += force/mass * time step
                        position += velocity * time step
                    ENDLOOP

which translates to the actual program code

                
                    FORALL i
                        f = c^2*(u[i-1] + u[i+1] – 2u[i])/h^2
                        v[i] = v[i] + f*dt
                        u_new[i] = u[i] + v[i]*dt
                    ENDFOR
                    u = u_new

This implementaion uses WebGL and was built with the help of webglfundamentals.org. Feel free to change the parameters.

Canvas height: Canvas width:

Initial water height:

Wave columns count:

(wave velocity, condition: c < h/dt)

(wave column width)

(damping scaling, condition: s < 1)

dt:

(simulation delta time, condition: dt < h/c)

Boundary condition:

Reflacting

Wraping

Create wave by:

Adding water

This changes the height of a column. There will be no water loss or gain because the implementation will add or substract water to the surrounding columns.

Applying force

This changes the velocity of a column. There will be water loss or gain. No implementation to stop this is in place.

Time between cycle calls (ms):

1D Height Field Fluid

Parameters

Simulation

Debug view

u array

v array