A GAS-LIQUID INTERFACE IS UNSTABLE WHEN SUBJECT TO DIFFERENTIAL VELOCITIES AND/OR ACCELERATIONS (BODY FORCES).    THE FORMER IS REFERRED TO AS KELVIN-HELMHOLTZ INSTABILITY (KHI), THE LATER AS RAYLEIGH-TAYLOR INSTABILITY (RTI).    SUCH AN UNSTABLE INTERFACE BECOMES WAVY AND EARLY GROWTH OF WAVES IS EXPONENTIAL.    THIS IS THE WELL-KNOWN LINEAR REGIME.

FURTHER DEVELOPMENT YIELDS THE NON-LINEAR REGIME OF GROWTH, AND EVENTUALLY THE INTERFACE BREAKS UP WHICH LEADS TO CHAOTIC MOTIONS AND COMPLEX PHASE CONFIGURATIONS; THAT IS TURBULENT MIXING.    THE LINEAR REGIME IS WELL-KNOWN IN THAT, FOR THE IDEAL CASES OF PARALLEL FLOW AND/OR NORMAL BODY FORCES, GIVEN AN INITIAL DISTURBANCE OF ANY PARTICULAR WAVELENGTH WE CAN PREDICT ITS GROWTH RATE IN THE LINEAR REGIME.

IN PRACTICE THE FASTEST-GROWING WAVE (S) WILL DOMINATE, BUT THIS MUST BE SELECTED BY NATURE FROM A WHOLE SPECTRUM OF INFINITESIMAL WAVES INITIALLY PRESENT, WHICH IN PRACTICE CANNOT BE KNOWN A PRIORI.    THE CANONICAL PROBLEM IN THIS RESPECT, A STEP UP FROM THE IDEAL CASES MENTIONED ABOVE, IS THAT OF A SPHERICAL LIQUID DROP SUDDENLY SUBJECTED TO THE BLAST BEHIND A SHOCK WAVE.    THE SUBJECT, KNOWN AS AEROBREAKUP, HAS CHALLENGED NUMERICAL SIMULATIONS FOR DECADES IN THAT EVEN THE MOST POPULAR METHODS RELY ON A MODEL OF THE INTERFACE AS A DIFFUSE REGION (DIM).

THE BASIC PREMISE OF OUR WORK IN THIS AREA IS THAT PREDICTION OF KHI INSTABILITIES WITH REAL FLUIDS (VISCOSITY, SHEAR FLOWS) IS SEVERELY COMPROMISED (IIA2007) BY SUCH DIFFUSE INTERFACE METHODS (DIM).    INSTEAD WE HAVE DEVELOPED THE SHARP-INTERFACE METHOD (SIM), WHICH WITH SECOND-ORDER ACCURACY, WAS SHOWN TO SATISFY LAX’S CRITERIA FOR CONVERGENCE OF WEAK SOLUTIONS; NAMELY CONSERVATION, CONSISTENCY, AND STABILITY (IIA2013).

WE HAVE SHOWN EXCELLENT AGREEMENT WITH EXPERIMENTS CARRIED OUT AT UNPRECEDENTED SPACE-TIME RESOLUTIONS AS NECESSARY FOR HIGH MACH FLOWS (IIA2008, IIA2011, IIA2013).    RECENTLY OUR CODE, ARMS-SIM (IIA2013), HAS BEEN EXTENDED TO 3D, AND WITH NEW EXPERIMENTS IN THE MAKING WE WILL REACH VALIDATION UP TO MACH 7 SHOCKS.

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