A method for simulating unsteady incompressible viscous flows on dynamic meshes within moving geometries is described. The numerical model is based on 2D Navier-Stokes incompressible unsteady flow solver on unstructured moving grid. A higher-order upwind characteristics-based finite volume scheme on unstructured grids and an implicit dual times stepping method are employed in the developed solver. A time accurate scheme for unsteady incompressible flows is achieved by using an implicit real-time discretization and dual time approach, which uses a technique similar to the artificial compressibility scheme. Furthermore, a general and robust moving mesh method has been developed to account for large deformation of the boundary geometry. In this method, a distance function, which itself is a combination of two other damping functions with the shortest distance of a node to the wall as the controlling parameter, is used to determine the displacement of every node of the mesh. The above moving scheme is further enhanced by a spring analogy method. This is equivalent to treating the mesh as a collection of interconnected springs with the inverse of the distance between two neighboring nodes as the stiffness coefficient. Flow in a two-dimensional channel with a moving indentation in one wall is studied to validate the method and the developed solver as a whole. A channel with moving indentation is chosen because it is considered to be a representative of physiological flow phenomena. It is observed that the dynamic mesh method is very robust and able to handle large deformation without excessive distortion of the dense mesh near the wall. Results of the simulation are compared with the corresponding experimental and previous numerical results and good agreement is observed.
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