In accordance with our Quality Policy, COMSOL maintains a library of hundreds of documented model examples that are regularly tested against the latest version of the COMSOL Multiphysics® software, including benchmark problems from ASME and NAFEMS, as well as TEAM problems.
Our Verification and Validation (V&V) test suite provides consistently accurate solutions that are compared against analytical results and established benchmark data. The documented models below are part of the COMSOL Multiphysics® software’s built-in Application Libraries. They include reference values and sources for a wide range of benchmarks, as well as step-by-step instructions to reproduce the expected results on your own computer. You can use these models not only to document your software quality assurance (SQA) and numerical code verification (NCV) efforts, but also as part of an in-house training program.
This example explores the shift in natural frequencies caused by changing the temperature. One study investigates a doubly clamped beam where both ends are fixed, while the other study looks at a cantilever beam where only one end is fixed. The following effects are studied: Stress ... Read More
This example describes the cooling and solidification, from melt to solid metal, in a continuous casting process. The model includes nonisothermal properties, temperature distribution, flow field, and phase change. This example uses the arbritrary Lagrangian-Eulerian method for modeling ... Read More
Many piezoelectric materials are ferroelectric. Ferroelectric materials exhibit nonlinear polarization behavior, such as hysteresis and saturation at large applied electric fields. In addition, the polarization and mechanical deformations in such materials can be strongly coupled due to ... Read More
This model example shows how to model nonlinear propagation of a cylindrical wave using the Nonlinear Pressure Acoustics, Time Explicit physics interface available in Acoustics Module of COMSOL Multiphysics. The interface implements the system of nonlinear acoustic equations in the form ... Read More
A plane electromagnetic wave propagating through free space is incident at an angle upon an infinite dielectric medium. This model computes the reflection and transmission coefficients and compares to the Fresnel equations. Read More
Homogeneous Charge Compression Ignition (HCCI) engines are being considered as an alternative to traditional spark- and compression-ignition engines. As the name implies, a homogeneous fuel/oxidant mixture is auto-ignited by compression with simultaneous combustion occurring throughout ... Read More
A square airbag made of a hyperelastic, compressible neo-Hookean material is inflated using pressurized air. Compressive stresses trigger wrinkling in some regions of the thin airbag. In this example, the wrinkling behavior is modeled using tension field theory, which gives a correct ... Read More
Simulation of Maxwell’s equations in the time domain is useful if the objective of the analysis is to observe a transient phenomenon, to find the time it takes a signal to propagate, or if the materials being modeled are non-linear with respect to the electric or magnetic field strength. ... Read More
Carbon dioxide in aqueous solution is highly corrosive and can cause significant damage to steel designs. Such conditions arise in pipes used in a variety of applications, especially within the petrochemical industry. In this tutorial example, turbulent flows consisting of carbon ... Read More
Ferroelectric materials exhibit nonlinear polarization behavior such as hysteresis and saturation at large applied electric fields. Many piezoelectric materials are ferroelectric. This model analyzes a simple actuator made of PZT piezoelectric ceramic material, which is subjected to ... Read More