Abstract:

Physics-based models of vapor-compression cycles are often formulated as large, stiff DAE systems with derivative discontinuities introduced at the points of phase change. We use an implementation of a discontinuity-aware ODE and DAE solver scheme that uses domain-specific, user-declared information to compute appropriate time steps for more efficient integration. This scheme is made opensource within DifferentialEquations.jl. We demonstrate how discontinuity information can be specified symbolically in a declarative modeling language such as Dyad and passed to the solver to address the numerical challenges posed. We apply this discontinuity-aware technique to two applications: First, a scalar ODE with two discontinuities, and then a model of a full vapor-compression cycle. The discontinuity-aware solver yields significantly fewer step rejections and improved solver times, particularly with the Rodas5P solver at loose tolerances, as compared to standard error control, suggesting that exposing physical discontinuity information from equation-oriented models to adaptive solvers can improve practical simulation performance without requiring reassembly of the model.