No abstract

Numerical methods for solving incompressible Navier-Stokes equations are widely applied and are among the most extensively studied. A plethora of approaches have been introduced targeting different applications and regimes; these methods vary in space discretization, choice of time integration scheme, or reduction of the non-linear equations to a sequence of simpler problems. While the theoretical properties of most of these variants are known, it is still difficult to pick the best option for a given problem, as practical performance of these methods has never been systematically compared over a varied set of geometries and boundary conditions.We introduce a collection of benchmark problems in 2D and 3D (geometry description and boundary conditions), including simple cases with known analytic solution, classical experimental setups, and complex geometries with fabricated solutions for evaluation of numerical schemes for incompressible Navier-Stokes equations in laminar flow regime. We compare the performance of a representative selection of most broadly used algorithms for Navier-Stokes equations on this set of problems. Where applicable, we compare the most common spatial discretization choices (unstructured triangle/tetrahedral meshes and structured or semi-structured quadrilateral/hexahedral meshes).The study shows that while the type of spatial discretization used has a minor impact on the accuracy of the solutions, the choice of time integration method, spatial discretization order, and the choice of solving the coupled equations or reducing them to simpler subproblems have very different properties. Methods that are directly solving the original equations tend to be more accurate than splitting approaches for the same number of degrees of freedom, but numerical or computational difficulty arise when they are scaled to larger problem sizes. Low-order splitting methods are less accurate, but scale more easily to large problems, while higher-order splitting methods are accurate but require dense time discretizations to be stable.We release the description of the experiments and an implementation of our benchmark, which we believe will enable statistically significant comparisons with the state of the art as new approaches for solving the incompressible Navier-Stokes equations are introduced.

We introduce a general differentiable solver for time-dependent deformation problems with contact. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed incremental potential contact method for handling contact and friction forces to solve PDE-and ODE-constrained optimization problems on scenes with a complex geometry. It support static and dynamic problems, it support differentiation with respect to all physical parameters involved in the physical problem description, which include shape, material parameters, friction parameters and initial conditions. Our analytically derived adjoint formulation is efficient, with an overhead of not more than 2 times the forward simulation, and shares many similarities with the forward problem, allowing reusing large parts of the code of an existing forward simulator code.We implement our approach on top of the open-source PolyFEM FE library, and demonstrate the applicability of our solver to shape design, initial condition optimization, and material estimation on both simulated results and in physical validations.

The sugarcane woolly aphid is one of the main pests of sugarcane worldwide. The Pinellia pedatisecta agglutinin (PPA) gene has been demonstrated to function towards aphid resistance in other crops. In our study, in order to investigate the PPA function towards aphid control in sugarcane and its underlying mechanism, the PPA gene was overexpressed in a sugarcane Zhongzhe 1 (ZZ1) cultivar in independent transgenic sugarcane lines. It was confirmed in this study that PPA transgenic sugarcane can resist aphids via detecting the aphids’ development and tracing the survival number on PPA−transgenic sugarcane lines as well as PPA negative control lines. The mechanism of PPA lectin−associated defense against aphids was preliminarily explored. Stomatal patterning differences of sugarcane leaves between PPA−transgenic sugarcane lines and negative control lines were found. PPA overexpression led to an increase in stomata number and a decrease in stomata size that might have changed the transpiration status, which is critical for aphids’ passive feeding. Moreover, the antioxidant enzyme, sugar, tannin and chlorophyll content in sugarcane leaves before and after aphid infestation was determined. The results indicated that PPA overexpression in sugarcane resulted in an increase in antioxidant enzyme activity and tannin content, as well as a reduction in the decline of certain sugars. These together may improve sugarcane resistance against the sugarcane woolly aphid.