gallleo / modia.jl

Domain Specific Extension of Julia for Modeling and Simulation

Modia

Modia is a domain specific extension of Julia for modeling and simulation of physical systems. The first version of Modia is planned to be uploaded in Summer 2017. Papers about Modia:

• Overview about Modia (ISoLA conference Oct. 2016).
• Overview and new features in Modia (12th International Modelica Conference, May 2017).
• New algorithms in Modia (12th International Modelica Conference, May 2017; slides in pptx and pdf format).
• Modia: A Domain Specific Extension of Julia for Modeling and Simulation (juliaCon 2017, June 2017; recording at YouTube)

Modia is designed to model and simulate physical systems (electrical, mechanical, thermo-dynamical, etc.) described by differential and algebraic equations. A user defines a model on a high level with model components (like a mechanical body, an electrical resistance, or a pipe) that are physically connected together. A model component is constructed by "expression = expression" equations. The defined model is symbolically processed (for example, equations might be analytically differentiated), JIT compiled and simulated with Sundials IDA solver with the KLU sparse matrix package. By this approach it's possible and convenient to build models with hundred thousands of equations describing the dynamics of a car, an airplane, a power plant, etc. and simulate them. The authors used previous experience from the design of the modeling language Modelica. Modia will also be used to design and evaluate features for future Modelica versions.

Component models are defined by @model macros. Such models contain definition of variables with various attributes such as start values, min, max, SI unit, etc. An @equations macro is used to define the equations of such a component. Coupling between components is expressed using a connect statement involving groups of variables. The semantics is either to constrain connected variables to be equal or to constrain a set of variables to sum to zero, for example to model Kirchhoff's current law.

"Hello world" Modia model:

# T*dx/dt + x = u(t)
#
using Modia
@model FirstOrder begin
   x = Variable(start=1)
   T = Parameter(0.5, "Time constant")
   u = 2.0 # Same as Parameter(2.0)
@equations begin
   T*der(x) + x = u
   end
end
result = simulateModel(FirstOrder, linspace(0,2,500))