Abstract

The simulation of engineering problems is quite often a complex task that can be time consuming. In this context, the use of Hyper Reduced Order Models (HROMs) is a promising alternative for real-time simulations. In this work, we study the design of HROMs for non-linear problems with a moving source. Applications to nonlinear phase change problems with temperature dependent thermophysical properties are particularly considered; however, the techniques developed can be applied in other fields as well.

A basic assumption in the design of HROMs is that the quantities that will be hyper-reduced are k-compressible in a certain basis in the sense that these quantities have at most k non-zero significant entries when expressed in terms of that basis. To reach the computational speed required for a real-time application, k must be small. This work examines different strategies for addressing hyper-reduction of the nonlinear terms with the objective of obtaining k-compressible signals with a notably small k. To improve performance and robustness, it is proposed that the different contributing terms to the residual are separately hyper-reduced. Additionally, the use of moving reference frames is proposed to simulate and hyper-reduce cases that contain moving heat sources. Two application examples are presented: the solidification of a cube in which no heat source is present and the welding of a tube in which the problem posed by a moving heat source is analysed.

Abstract

We present a conservative second order staggered time scheme for dry and moist variable density air flow implemented in the open source CFD solver code saturne. The staggered time arrangement introduced by Pierce and Moin [1] is extended to finite volumes and discontinuous solutions. An Helmholtz equation is solved in order include the thermodynamical pressure variation and to remove the acoustic CFL restriction. The internal energy equation supplemented by a corrective source term based on the kinetic energy dissipation [2] is solved, allowing the scheme to be consistent with discontinuous solutions. The water phase change is treated by considering thermodynamical equilibrium. Dalton’s law is used to compute the density and the temperature is obtained from the internal energy equation, solving with Newton’s method in case of phase change. A numerical analysis is presented to insure the positivity of the thermodynamic variables, followed by the scheme verification and validation. First, dry air cases are presented: a natural convection and shock cases are used to verify its accuracy related to singularities and buoyancy effects. Moreover, a pressure cooker like system shows the scheme good reproduction of pressure variations and correct time error convergences rates. Finally, the moist air module is verified against analytical cases.