Real Time Visual Simulation of Smoke on the GPU

By Muhammad S. KarimMSCS Student

Department of Computer ScienceThe University of New Mexico

Introduction & MotivationHORVATH, C., AND GEIGER, W. 2009. Directable, high-resolution

simulation of fire on the GPU. ACM Trans. Graph. 28, 3, 1-8.Used in creating visual effects in “Harry Potter and the Half Blood

Prince”.Uses a incompressible, inviscid Navier-stokes equations for fluid flow.Pursuing as part of an Individual Study project with Dr. Joe Kniss.

The Project and GoalStarting with an implantation of the following:FEDKIW, R., STAM, J., AND JANSEN H. W. 2001. Visual

Simulation of Smoke. In proc. of ACM SIGGRAPH 2001.Based on: Stam, J. 1999. Stable Fluids. In SIGGRAPH 99.Goal is to pursue the real-time implementation using GPU

specific vertex & fragment processing features.

Images from [FEDKIEW 2001]

Equations of Fluid FlowUsing incompressible and inviscid (leaving out the viscausity

term) form of Navier-Stokes equations for fluid flow:

u=velocity, p=pressure, f=force

Smoke properties (scalar fields): a. Density (ρ), b. Temperature (T)

Simulation Algorithm, inside a 3D grid:Step 1: Add Forces (Buoyancy, Vorticity)Step 2: Advect Velocity FieldStep 3: Solve for intermediate pressure term. Step 4: Project velocity field to make the field divergence free.Step 5: Apply boundary conditions to Velocity & Pressure fields.Step 6: Advect, Dissipate scalar fields (Density & Temperature)

u = Velocityp = Pressuref = Forcet = Time

Mass Conservation

Momentum Conservation

Simulation Algorithm Steps1.a Add Buoyant force to the velocity field:

+ =

Shader

u(t) F(buoy)

u’(t)

ρ(t) T(t)

*Tamb

Simulation Algorithm Steps1.b Add back Vorticity Confined Force to the velocity field:

+ =

u(t) Fvort u’(t)

Curl(u)

Shader

Simulation Algorithm Steps2. Advect Velocity field: (Semi-Lagrangian Advection)Move back along the vector back a timestep.Pick a vector by Tri-linear interpolating the 6 neighboring cells

from the 3D texture. Set this computed value to the current cell.]Benefits: ‘Stable’ field, avoid “blow-ups”, GPU friendly.

u(t) u’(t)

Shader

Simulation Algorithm Steps3. Compute field Pressure (for the next projection

step): u(t)

Shader

Div(u)

ShaderIterative

Jacobi Solver

p(t) after N Jacobi Iterations(I use 30-40)

Solve for p

Simulation Algorithm Steps4. Project Velocity field:Using Helmholtz-Hodge decomposition. (To ensure 0

divergence). Any vector field u* can be uniquely decomposed as the

following equation where u has 0 divergence:

u(t)u (t+1)

= -

Grad ( p(t) )

Simulation Algorithm Steps5. Apply boundary conditions:Based on ‘fixed-grid’, fluid confined to the grid.a. Velocity goes to zero on the boundary (no-slip condition).b. Pressure derivative goes to zero on the boundary.

(Neumann pressure condition).

Draw 4 lines along the boundary on each slice of the 3D texture

Draw a quad on the front (z=0) and another on the back (z=slices-1) of the 3D texture

GPU Implementation

Simulation Algorithm Steps6. Advect the scalar fields (Density & Temperature)Similar to velocity field advection.Dissipate the scalar fields based on time.

Shader

Shader

u(t)

ρ(t)

T(t)

Volume Renderinga. Slice the grid region from the viewer’s point-of-view.b. Render each slice from front-to-back order.c. Use the “under” operator to composite (blend) the slices to make

the final images of the smoke region. I used the polygon slicing algorithm implemented in a vertex

shader exactly described in: Ref “Real-time Volume Graphics” – Engel et. al. Ch-3.5.

Demonstration from my programshowing 2 slices

Volume Rendering (more…) Implemented volumetric shadows using the Half-Angle

Slicing technique by Kniss et al. 2003. Ref: Kniss, J., S. Premo e, C. Hansen, P. Shirley, and A. McPherson. 2003.

"A Model for Volume Lighting and Modeling." IEEE Transactions on Visualization and Computer Graphics 9(2), pp. 150–162.

Using a 2D light buffer to accumulate opacity at each slice, the use as a shadow map

Some ResultsSelf-shadowing the smoke volume produces more realism.Smoke volume transparency is computed based on the

smoke density values computed in the grid.

No self-showing inside the volume

With self-showing inside the volume

Closing Remarks and Demo I used 64 x 64 x 64 grids in the Demo, higher resolution

provides finer details. I also used a fixed grid, will possibly explore techniques to

move the fluid out of the box.Practical and possible to use in real-time applications with

mid-high end GPUs.