Numerical simulations
A gallery of numerical experiments in fluid dynamics, shock waves, and multiphysics.
These examples illustrate structure-preserving and stabilized methods for challenging partial differential equations. Select a simulation for numerical details, or play an available animation.
01
Compressible flows and shock waves
High-speed flows with shocks, contact discontinuities, and complex wave interactions.
Explosion in a closed domain
A strong circular shock interacts repeatedly with internal cylinders and the outer wall.
Mach 10 double-Mach reflection
Shock reflection and fine-scale structures in a high-Mach-number wind tunnel.
Supersonic flow around a cylinder
Bow shocks, reflected waves, separation, and vortical structures downstream of a cylinder.
Circular Riemann problem
An expanding shock, contact discontinuity, and rarefaction generated by radial initial data.
Implosion problem
Interacting shocks produced by low-density, low-pressure gas inside a diamond-shaped region.
02
Incompressible and variable-density flows
Turbulent and stratified flows computed with stabilized continuous finite element methods.
Turbulent flow around a car
Implicit large-eddy simulation of the turbulent wake behind a full Volvo car geometry.
Variable-density lock exchange
Density, vorticity, and artificial viscosity in a gravity-driven lock-exchange flow.
03
Geophysical and atmospheric flows
Surface quasi-geostrophic simulations of vortex interactions and multiscale turbulence.
Freely decaying SQG turbulence
Starting from noisy buoyancy data, small vortices emerge, interact, and merge into larger coherent structures.
Double-vortex SQG interaction
Two rotating vortices generate a sharp filamentary layer while remaining distinct over long times.
04
Magnetohydrodynamics and fusion plasmas
Structure-preserving simulations of strongly magnetized, compressible flows.
Orszag–Tang vortex
Density evolution in a canonical MHD benchmark with interacting shocks and vortical structures.
Astrophysical MHD jet
A Mach 800 magnetized jet propagating into an ambient fluid under a strong background field.
05
Kinetic plasma simulations
Phase-space dynamics computed with stabilized and positivity-preserving Vlasov solvers.
Bump-on-tail instability
Nonlinear phase-space vortices generated by a fast particle population interacting with a plasma wave.
Multi-vortex two-stream instability
Fine vortex structures produced by counter-streaming particle populations while preserving positivity.
06
Multiphysics and other PDE models
Numerical experiments beyond classical fluid dynamics, including moving interfaces and solidification.
Isotropic phase-field solidification
Phase-field evolution for the solidification of water on a million-node finite element mesh.
Anisotropic phase-field solidification
Direction-dependent crystal growth generated by an anisotropic phase-field model.