Fluid Simulation with Anisotropic Pressure Segregation and Time-Dependent Tensor Fields

We propose a mathematical and computational model to address an anisotropic incompressible fluid transport problem. Our method aims to modulate the pressure and viscosity terms using a symmetric positive-definite second-order tensor field that can vary both spatially and temporally. We introduce an anisotropic projection step designed to accumulate and adjust pressure as the tensor field changes over time. This step relies on a velocity update scheme that ensures the divergence-free nature of the velocity field even as the tensor field varies through time. Also, we propose a novel tensor-based particle advection scheme based on the Explicit Integration following the Velocity and Acceleration Streamline (X-IVAS) method, implemented within an extended Marker-and-Cell (MAC) grid. Our method is unconditionally stable and presents suitable accuracy for designing incompressible fluid behavior. The experimental results show how anisotropic tensor fields modulate the pressure field, thereby influencing the behavior of the fluid flow.