Uncertainty Reduction for Model Error Detection in Multiphase Shock Tube Simulation

Uncertainty quantification (UQ) is an important step in the verification and validation of scientific computing. Validation is often inconclusive when uncertainty is larger than an acceptable range for both simulation and experiment. Therefore, uncertainty reduction (UR) is important to achieve meaningful validation. A unique approach in this paper is to separate model error from uncertainty such that UR can reveal the model error. This paper aims to share lessons learned from UQ and UR of a horizontal shock tube simulation, whose goal is to validate the particle drag force model for the compressible multiphase flow. Firstly, simulation UQ revealed the inconsistency in simulation predictions due to the numerical flux scheme, which was clearly shown using the parametric design of experiments. By improving the numerical flux scheme, the uncertainty due to inconsistency was removed, while increasing the overall prediction error. Secondly, the mismatch between the geometry of the experiments and the simplified 1D simulation model was identified as a lack of knowledge. After modifying simulation conditions and experiments, it turned out that the error due to the mismatch was small, which was unexpected based on expert opinions. Lastly, the uncertainty in the initial volume fraction of particles was reduced based on rigorous UQ. All these UR measures worked together to reveal the hidden modeling error in the simulation predictions, which can lead to a model improvement in the future. We summarized the lessons learned from this exercise in terms of empty success, useful failure, and deceptive success.

A compressible multiphase flow model for violent aerated wave impact problems

This paper focuses on the numerical modelling of wave impact events under air entrapment and aeration effects. The underlying flow model treats the dispersed water wave as a compressible mixture of air and water with homogeneous material properties. The corresponding mathematical equations are based on a multiphase flow model which builds on the conservation laws of mass, momentum and energy as well as the gas-phase volume fraction advection equation. A high-order finite volume scheme based on monotone upstream-centred schemes for conservation law reconstruction is used to discretize the integral form of the governing equations. The numerical flux across a mesh cell face is estimated by means of the HLLC approximate Riemann solver. A third-order total variation diminishing Runge–Kutta scheme is adopted to obtain a time-accurate solution. The present model provides an effective way to deal with the compressibility of air and water–air mixtures. Several test cases have been calculated using the present approach, including a gravity-induced liquid piston, free drop of a water column in a closed tank, water–air shock tubes, slamming of a flat plate into still pure and aerated water and a plunging wave impact at a vertical wall. The obtained results agree well with experiments, exact solutions and other numerical computations. This demonstrates the potential of the current method to tackle more general wave–air–structure interaction problems.