An Efficient RBF Dynamic Mesh Method for Continuous Moving Boundary Problems

TO ADDRESS THE CHALLENGES OF LOW COMPUTATIONAL EFFICIENCY AND MESH QUALITY DETERIORATION IN DYNAMIC MESH METHODS FOR CONTINUOUS MOVING BOUNDARY PROBLEMS—SUCH AS ABLATION AND FLUID–STRUCTURE INTERACTION—THIS PAPER PROPOSES TWO EFFICIENT AND ROBUST ENHANCED STRATEGIES BASED ON THE RADIAL BASIS FUNCTION (RBF) METHOD. THE FIRST STRATEGY INTEGRATES AN IMPROVED GREEDY ALGORITHM, INCORPORATING MULTI-POINT ADDITION AND A MINIMUM DISTANCE CONSTRAINT, TO ACCELERATE CONTROL POINT SELECTION. IT SIMPLIFIES PARAMETER CONFIGURATION BY FIXING THE INITIAL MESH SCALING FACTOR AND INCORPORATES LIGHT LAPLACIAN SMOOTHING TO CORRECT LOCAL DISTORTIONS. THE SECOND STRATEGY ACHIEVES LOCALIZED LAYER-WISE DISPLACEMENT PROPAGATION BASED ON CELL TOPOLOGY. STARTING FROM THE MOVING BOUNDARY NODES, IT COMPUTES THE DISPLACEMENT OF NEIGHBORING NODES VIA RBF AND PROPAGATES INWARD LAYER BY LAYER. A DISPLACEMENT THRESHOLD IS APPLIED TO TERMINATE ADJUSTMENTS FOR NODES WITH MINIMAL MOTION, AND GLOBAL SMOOTHING IS SUPPLEMENTED TO ENSURE MESH QUALITY. VALIDATION USING A SPHERICAL-HEAD CYLINDER ABLATION CASE DEMONSTRATES THAT THE PROPOSED METHODS SIGNIFICANTLY IMPROVE COMPUTATIONAL EFFICIENCY WHILE MAINTAINING HIGH MESH QUALITY. ADDITIONALLY, THEY ARE SUCCESSFULLY COUPLED WITH A HEAT FLUX–TEMPERATURE–ABLATION SOLVER TO SIMULATE A 400-SECOND ABLATION PROCESS. THE RESULTS INDICATE THAT THE PRESENT APPROACH PROVIDES AN EFFICIENT AND RELIABLE DYNAMIC MESH SOLUTION FOR CONTINUOUS MOVING BOUNDARY PROBLEMS.