DEVELOP A SECOND ORDER PARTICLE-IN-CELL METHOD FOR A 2D EULERIAN FINITE DIFFERENCE CODE

THE MOST DIFFICULT PROBLEM IN ANALYZING IMPACT DYNAMICS OR EXPLOSIVE ACCELERATION OF METALS IN WARHEAD DESIGN AND ANALYSIS IS TO EXPLICITLY MODEL THE VOIDS DEVELOPED IN THE MATERIAL DUE TO SPALLING OR FRACTURING, OR THE MULTIMATERIALS INTERFACE MOVEMENTS DUE TO MIXED MATERIALS OCCURRING IN THE EULERIAN SPACE. TO OVERCOME THIS PROBLEM, ISI PROPOSES TO DEVELOP A SECOND ORDER PARTICLE-IN-CELL (PIC) METHOD BASED ON AN EULERIAN FINITE DIFFERENCE FORMULATION TO TREAT THE VOIDS AND MULTIMATERIAL INTERFACE PROBLEMS. THE FORTRAN CODE PREPARED FOR IMPLEMENTING THE SECOND ORDER PIC METHOD WILL BE INITIALLY FORMULATED AND TESTED IN THE EULERIAN FINITE DIFFERENCE CODE PICEP2D. THE FORMULATION OF THE FORTRAN CODE WILL BE IN MODULIZED FORMAT SO THAT IT CAN BE EASILY INCORPORATED INTO OTHER EXISTING EULERIAN FINITE DIFFERENCE CODE SUCH AS AIR FORCE ARMAMENT LABORATORY'S EULERIAN FINITE DIFFERENCE CODE, HULL, TO SAVE CODE MAINTENANCE COST. IN THE SECOND ORDER PIC METHOD THE MATERIALS IN EACH CELL ARE REPRESENTED BY A NUMBER OF DISCRETE LUMPED MASS POINTS OR PARTICLES TO MODEL THE MATERIAL DISCONTINUITIES SUCH AS VOIDS OR MULTIMATERIAL MIXING OCCURRING IN EACH CELL OF THE FINITE DIFFERENCE MESH. TO ENHANCE THE COMPUTATIONAL EFFICIENCY, THE NUMBER OF PARTICLES WILL BE DYNAMICALLY ADJUSTED (IE. CREATED OR ELIMINATED) ACCORDING TO THE PHYSICS OF THE PROBLEM. TO OPERATOR SPLITTING COMPUTATIONAL PROCEDURE WILL BE USED TO MAINTAIN THE NUMERICAL ACCURACY OF THE ONE-DIMENSIONAL PROCEDURE. IN THE OPERATOR SPLITTING COMPUTATIONAL PROCEDURE THE EQUATIONS-OF-MOTION ARE SOLVED IN THE ALTERNATING COORDINATE DIRECTIONS FOR EACH TIME STEP ADVANCEMENT.