Collaborative Research: New Formulation and Algorithms for Fluid-Structure Interaction, with Application to Tumor Growth

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Fluid-structure interaction (FSI) problems play prominent roles in many scientific and engineering fields, yet an accurate study of such problems remains highly challenging due to the strong nonlinearity and multi-physics involved. Current computational theory and methods for fluid-structure interactions lack sufficient accuracy and realistic material representations, and are limited to relatively simple structural configurations. The goal of this project is to overcome such limitations by establishing a new computational mathematical framework for accurate and efficient numerical investigation of complex FSI problems, particularly for tumor growth modeling and simulation. The PIs will derive new mathematical formulation that allows the study of general FSI problems with sophisticated structural settings, develop efficient numerical algorithms that ensure high accuracy in FSI computations, and apply the proposed mathematical formulation and computational methods to the individual-cell-based modeling and simulation of tumor growth. This proposal builds on the PIs? solid background in computational and applied mathematics and significant work on tumor modeling.The proposed research will improve the understanding of the nonlinear dynamics in highly complex FSI problems through a combined mathematical and computational framework. Experimental measurements will also be used for validating the numerical results. The success of this project will not only provide a solid knowledge base for advancing the current state of computational FSI study, but also enable important discoveries in the fundamental mechanism of early tumor formation and development. The project experiences and findings will strengthen the research collaboration and curriculum development in computational mathematics and mathematical biology at both Old Dominion University and the College of William and Mary. Due to the close geographical proximity between the two schools, project impacts will be maximized through convenient communication between faculty and students and through joint programs between the two schools. Education and outreach activities will involve graduate and undergraduate students in the theory, methods and application of computational mathematics.