New math formula fixes a decades-old computing problem in fluid dynamics
Researchers have solved a fundamental challenge in simulating fluids with varying densities—a problem that has plagued computational engineers for years. The breakthrough enables faster, more accurate predictions for everything from oil pipelines to chemical reactors, potentially reducing design time and improving safety across industries reliant on fluid dynamics modeling.
Originaltitel: A fully conservative and shift-invariant formulation for Galerkin discretizations of incompressible variable density flow
<p>This paper introduces a formulation of the variable density incompressible Navier-Stokes equations by modifying the nonlinear terms in a consistent way. For Galerkin discretizations, the formulation leads to favorable discrete conservation properties without the divergence-free constraint being strongly enforced. In addition, the formulation is shown to make the density field invariant to global shifts. The effect of viscous regularizations on conservation properties is also investigated. Numerical tests validate the theory developed in this work. The new formulation shows superior performance compared to other formulations from the literature, both in terms of accuracy for smooth problems and in terms of robustness.</p>