Guide to PETSc Tutorial Examples, by Physics#
Below we list examples which simulate particular physics problems so that users interested in a particular set of governing equations can easily locate a relevant example. Often PETSc will have several examples looking at the same physics using different numerical tools, such as different discretizations, meshing strategy, closure model, or parameter regime.
Poisson#
The Poisson equation
is used to model electrostatics, steady-state diffusion, and other physical processes. Many PETSc examples solve this equation.
- Finite Difference
- 2D
- 3D
- Finite Element
Elastostatics#
The equation for elastostatics balances body forces against stresses in the body
where \(\bm\sigma\) is the stress tensor. Linear, isotropic elasticity governing infinitesimal strains has the particular stress-strain relation
where the strain tensor \(\bm \varepsilon\) is given by
where \(\bm u\) is the infinitesimal displacement of the body.
- Finite Element
If we allow finite strains in the body, we can express the stress-strain relation in terms of the Jacobian of the deformation gradient
and the right Cauchy-Green deformation tensor
so that
In the example itself, everything can be expressed in terms of determinants and cofactors of \(F\).
- Finite Element
Stokes#
The Stokes equations
describe slow flow of an incompressible fluid with velocity \(u\), pressure \(p\), and body force \(f\).
- Finite Element
See Guide to the Stokes Equations using Finite Elements in PETSc for more.
Euler#
Heat equation#
The heat equation
is used to model heat flow, time-dependent diffusion, and other physical processes.
- Finite Element
- 2D
- 3D