John A. Trapp

A CHOKED-FLOW CALCULATION CRITERION FOR NONHOMOGENEOUS, NONEQUILIBRIUM, TWO-PHASE FLOWS

Abstract This study applies the theory of characteristics to a one-dimensional transient model, in order to analyze the conditions for a choked, two-phase flow. The basic hydrodynamic model analyzed is a two-fluid model that includes relative phasic acceleration terms and a nonequilibrium, derivative-dependent exchange of mass. The analytical results provide an algebraic, choked-flow criterion analogous to that for a single-phase flow, except that terms pertaining to relative phase motion and nonequilibrium mass transfer are included. This paper discusses the numerical implementation of the choked-flow criterion in a nonhomogeneous and nonequilibrium finite difference scheme. The use of a mass-transfer model having a derivative dependence is shown to be necessary if self-choking is expected.

Early partial systolic closure of the pulmonic valve relates to severity of pulmonary hypertension

Ultrasound studies in pulmonary hypertension often show systolic partial closure of the pulmonic valve and early peaking of Doppler pulmonary flow velocity, but these findings are poorly understood. Our initial observations of earlier systolic partial closure with higher pulmonary pressures suggested that this phenomenon might relate to pressure. In 30 patients with documented pulmonary hypertension, the timing of systolic partial closure and the corresponding decrease in Doppler flow velocity related inversely to pulmonary artery pressure at catheterization. Peak flow preceded the systolic velocity decrease and also related inversely to pressure. Since changing flow velocity might reflect a changing driving force across the valve, we examined simultaneous high-fidelity catheter pressure tracings from the right ventricle and pulmonary artery from 24 patients with and without pulmonary hypertension. In 30 studies, a positive right ventricular to pulmonary artery pressure gradient was present early in systole, but the gradient decreased to a minimum value in mid-to-late systole. The timing of this minimum also related inversely to pressure. We conjectured that forces opposing ejection occur earlier in pulmonary hypertension, thereby decreasing the forward driving force and allowing earlier partial systolic closure.

A nearly-implicit hydrodynamic numerical scheme for two-phase flows

This article presents an extension of the semi-implicit numerical scheme for two-phase flow simulation. The extension uses an implicit evaluation of the convective fluxes and thus eliminates the material Courant stability restriction. The new algorithm involves a two-step approach for the mass and energy equations and a single fully-implicit step for the momentum evaluations. Some analysis and accuracy considerations for the scheme are also presented.

Effective Constrained Dynamic Simulation Using Implicit Constraint Enforcement

Stable and effective enforcement of hard constraints is one of the crucial components in controlling physics-based dynamic simulation systems. The conventional explicit Baumgarte constraint stabilization confines the time step to be within a stability limit and requires users to pick problem-dependent coefficients to achieve fast convergence or to prevent oscillations. The recently proposed post-stabilization method has shown a successful constraint drift reduction but it does not guarantee the physically correct behavior of motion and requires additional computational cost to decrease the constraint errors. This paper presents our new implicit constraint enforcement technique that is stable over large time steps and does not require problem dependent stabilization parameters. This new implicit constraint enforcement method uses the future time step to estimate the correct magnitude of the constraint forces, resulting in better stability over bigger time steps. More importantly, the proposed method generates physically conforming constraint forces while minimizing the constraint drifts, resulting in physically correct motion. Its asymptotic computational complexity is same as the explicit Baumgarte method. It can be easily integrated into various constrained dynamic systems including rigid body or deformable structure applications. This paper describes a formulation of implicit constraint enforcement and an accumulated constraint error and dynamic behavior analysis for comparison with existing methods.

The mean flow character of two-phase flow equations

Abstract This study examines the nature of the one-dimensional mean motion description for two-phase flows. It is conjectured that the unstable wave growth in a streaming two-phase flow with unequal phasic velocities is a result of the failure to model the correlations of the fluctuating velocity components in the momentum equations. A general functional form for these velocity correlations is derived based upon invariance and dimensional arguments. Some speculative closure models using this functional form are derived and it is shown that reasonable forms of this closure model do in fact lead to a stable mean motion description.

Implicit constraint enforcement for rigid body dynamic simulation

The paper presents a simple, robust, and effective constraint enforcement scheme for rigid body dynamic simulation. The constraint enforcement scheme treats the constraint equations implicitly providing stability as well as accuracy in constrained dynamic problems. The method does not require ad-hoc problem dependent parameters. We describe the formulation of implicit constraint enforcement for both holonomic and non-holonomic cases in rigid body simulation. A first order version of the method is compared to a first order version of the well-known Baumgarte stabilization.

Parameter-free second-order numerical scheme for constrained multibody dynamic systems

This paper describes a second-order numerical scheme for constrained multibody dynamics that is simple to implement and does not require the selection of parameters for constraint satisfaction. The method is a predictor-corrector type of method, and both the predictor and the corrector steps require solution of a symmetric positive-definite linear system with no iteration of nonlinear equations. The basic philosophy of the method is to satisfy the constraint equations to the same order as the discretization of the ordinary differential equations.