Flux limiting for hyperbolic systems requires a careful generalization of the design principles and algorithms introduced in the context of scalar conservation laws. In this chapter, we develop FCT-like algebraic flux correction schemes for the Euler equations of gas dynamics. In particular, we discuss the construction of artificial viscosity operators, the choice of variables to be limited, an...

State-to-state numerical simulations of high-speed reacting flows are the most detailed but also often prohibitively computationally expensive. In this work, we explore usage machine learning algorithms to alleviate such a burden. Several tasks have been identified. Firstly, data-driven regression models were compared for prediction relaxation source terms appearing in right-hand side state-to-...

In this paper, we describe an integral equation approach for simulating diffusion problems with moving interfaces. The solutions are represented as moving layer potentials where the unknowns are only defined on the interfaces. The resulting integro-differential equation (IDE) system is solved using spectral deferred correction (SDC) techniques developed for general differential algebraic equati...

We develop a forward modelling algorithm for computing time domain electromagnetic responses for conductive, permeable bodies in the low frequency regime. Both physical properties can be highly discontinuous. The parameter regimes considered give rise to highly stiff problems in the time domain and an implicit method, backward Euler, is used for time-stepping. At each time step the electromagne...

In this paper, we prove the energy diminishing of a normalized gradient flow which provides a mathematical justification of the imaginary time method used in physical literatures to compute the ground state solution of Bose-Einstein condensates (BEC). We also investigate the energy diminishing property for the discretization of the normalized gradient flow. Two numerical methods are proposed fo...

A 'fictitious boundary method' for computing incompressible flows with complicated small-scale and/or time-dependent geometric details is presented. The underlying technique is based on a special treatment of Dirichlet boundary conditions , particularly for FEM discretizations, together with so-called 'iterative filtering techniques' in the context of hierarchical multigrid approaches such that...

The unstable flow with rotating-stall-like (RS) effects in a rotor-cascade of an axialcompressor was numerically investigated. The RS was captured with the reduction in mass flow rateand increasing of exit static pressure with respect to design operating condition of the single rotor.The oscillatory velocity traces during the stall propagation showed that the RS vortices repeatperiodically, and...

Abstract Model order reduction (MOR) methods enable the generation of real-time-capable digital twins, with potential to unlock various novel value streams in industry. While traditional projection-based are robust and accurate for linear problems, incorporating machine learning deal nonlinearity becomes a new choice reducing complex problems. These kinds independent numerical solver full model...

FastOpt’s new automatic differentiation tool TAF is applied to the two-dimensional Navier-Stokes solver NSC2KE. For a configuration that simulates the Euler flow around a NACA airfoil, TAF has generated the tangent linear and adjoint models as well as the second derivative (Hessian) code. Owing to TAF’s capability of generating efficient adjoints of iterative solvers, the derivative code has a ...

A scheme for the twedimensional Euler equations that uses flow parameters to determine the direction for upwind-differencing is described. This approach reduces the grid-dependence of conventional schemes. Upwinding at the local flow angle and the local pressure-gradient angle is tested. The upwindbiased fluxes are calculated with Roe's approximate Riemann solver. A centered flux is used for th...