NUMERICAL SIMULATIONS OF MULTIPHASE FLOWS IN PRACTICE RELY ON MODELS THAT REPRESENT LOCAL CONDITIONS IN SOME AVERAGE WAY.    THUS EACH PHASE (GAS, LIQUID, OR SOLID) BECOMES AN EFFECTIVE FIELD THAT INTERACTS WITH ALL OTHER FIELDS PRESENT IN SOME AVERAGE FASHION.    KNOWN FOR MORE THAN A CENTURY, SUCH EFEFCTIVE-FIELD MODELS (EFM) SUFFER FROM A SERIOUS MATHEMATICAL SHORTCOMING; NAMELY THEY FAIL THE HYPERBOLIC CHARACTER THAT PHYSICAL SYSTEMS OF THIS TYPE ARE KNOWN TO POSSESS.

THE PRACTICAL CONSEQUENCE IS THAT NUMERICAL IMPLEMENTATIONS ARE UNSTABLE AND LITERALLY BLOW UP, UNLESS ONE RESORTS TO ARBITRARY MEANS TO DUMP THE NUMERICAL INSTABILITIES.    THESE INCLUDE AD HOC TERMS ADDED TO THE SYSTEM OF EQUATIONS OR INCREASING THE SIZE OF THE NUMERICAL NODES SUFFICIENTLY TO ALLOW NUMERICAL DIFFUSION DUMP THE SPIKES.

FOR MANY PROBLEMS SUCH APPROACHES HAVE PROVEN ADEQUATE AND EFMs ARE USED EXTENSIVELY, EVEN THOUGH THERE IS ALSO A SIGNIFICANT AMOUNT OF MISUSE (FOR EXAMPLE COUNTING NUMERICAL INSTABILITIES AS “PHYSICS” IN FLOW REGIME TRANSITIONS).    FOR MANY OTHER PROBLEMS SUCH FIXES ARE SIMPLY IMPOSSIBLE.

IN PARTICULAR THIS IS THE CASE FOR THE CLASS OF PROBLEMS (OUR FOCUS HERE) INVOLVING SHOCK WAVES, HIGH RELATIVE VELOCITIES (CONTINUOUS PHASE COMPRESSIBLE, DISPERSE PHASE HEAVY), AND STEEP VARIATIONS OF A DISPERSE PHASE VOLUME FRACTION (EDP16, EDP17).    WITH SOLID PARTICLES AS THE DISPERSE PHASE DEFINES FOR US A CANONICAL PROBLEM IN THIS AREA OF MULTIPHASE FLOWS IN THAT DESPITE APPARENT SIMPLICITY IT CONTAINS ALL KEY INGEDIENTS NEEDED TO ADDRESS THE NON-HYPRBOLICITY ISSUE NOTED ABOVE AND TO RIGOROUSLY EXPLORE THE UNDERLYING PHYSICS (EDP13); THUS GUIDING FUNDAMENTAL FIXES TO THE EFMs (EDP13).

MORE SPECIFICALLY WE ARE LOOKING BEYOND A REDUCTIONIST APPROACH WHEREBY THE COMPOSITE BEHAVIOR CANNOT BE ACCESSED BY ACCOUNT FOR SINGLE-PARTICLE (IN A FLUID) MOMENTUM TRANSFERS IN A STANDARD EFM.    INSTEAD THE MODEL ITSELF MUST BE INFORMED TO YIELD THE MULTIPHASE INTERACTIONS THAT OBSERVE THE PHYSICS (EDP18).