Fluid simulation with anisotropic pressure segregation and time-dependent tensor fields

Abstract

The inherent anisotropy of multiple complex flows of natural and engineered systems is still a challenge when it comes to accurately modeling and simulating their behavior. Our focus lies in investigating the anisotropic modulation of pressure and evaluating its impact on fluid flow. To this end, tensor fields emerge as a crucial mathematical tool that enables the simulation of anisotropic effects. The objective of this work is to develop a mathematical and computational model capable of addressing anisotropic fluid transport problems. Our proposed model 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 a novel anisotropic projection step designed to accumulate and adjust pressure as the tensor field evolves 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 undergoes temporal variations. Additionally, we propose a novel tensor-based anisotropic 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. We present a series of experiments to evaluate the behavior of fluid flow under various configurations of tensor fields. These experiments are divided into constant tensor fields and time-dependent tensor fields. Furthermore, we showcase an experiment that demonstrates how a body force, based on the divergence of the current tensor field configuration, can be utilized to influence fluid flow. The experimental results highlight how anisotropic tensor fields modulate the pressure field, thereby influencing the behavior of the fluid flow. These experimental results demonstrate our method’s numerical stability and suitable accuracy for generating visual effects. Finally, we present an overall discussion of our method capabilities, future works, and possible applications over visualization.