A High Order Bound Preserving Finite Difference Linear Scheme for Incompressible Flows

We propose a high order finite difference linear scheme combined with a high order bound preserving maximum-principle-preserving (MPP) flux limiter to solve the incompressible flow system. For such problem with highly oscillatory structure but not strong shocks, our approach seems to be less dissipative and much less costly than a WENO type scheme, and has high resolution due to a Hermite reconstruction. Spurious numerical oscillations can be controlled by the weak MPP flux limiter. Numerical tests are performed for the Vlasov-Poisson system, the 2D guiding-center model and the incompressible Euler system. The comparison between the linear and WENO type schemes, with and without the MPP flux limiter, will demonstrate the good performance of our proposed approach.     

A Priori Subcell Limiting Approach for the FR/CPR Method on Unstructured Meshes

A priori subcell limiting approach is developed for high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) methods on two-dimensional unstructured quadrilateral meshes. Firstly, a modified indicator based on modal energy coefficients is proposed to detect troubled cells, where discontinuities exist. Then, troubled cells are decomposed into nonuniform subcells and each subcell has one solution point. A second-order finite difference shock-capturing scheme based on nonuniform nonlinear weighted (NNW) interpolation is constructed to perform the calculation on troubled cells while smooth cells are calculated by the CPR method. Numerical investigations show that the proposed subcell limiting strategy on unstructured quadrilateral meshes is robust in shock-capturing.     

Effects of anteriorly-loaded treadmill walking on dynamic gait stability in young adults

BackgroundAnteriorly-loaded walking is common in many occupations and may increase fall risk. Dynamic gait stability, defined by the Feasible Stability Region (FSR) theory, quantifies the kinematic relationship between the body’s center of mass (COM) and base of support (BOS). FSR-based dynamic gait stability has been used to evaluate the fall risk.Research questionHow does front load carriage affect dynamic gait stability, step length, and trunk angle among young adults during treadmill walking?MethodsIn this between-subject design study, 30 healthy young adults were evenly randomized into three load groups (0%, 10%, or 20% of body weight). Participants carried their assigned load while walking on a treadmill at a speed of 1.2 m/s. Body kinematics were collected during treadmill walking. Dynamic gait stability (the primary variable) was calculated for two gait events: touchdown and liftoff. Step length and trunk angle were measured as secondary variables. One-way analysis of variance was conducted to detect any group-related differences for all variables. Post-hoc analysis with Bonferroni correction was performed when main group differences were found.ResultsNo significant differences but medium to large effect sizes were found between groups for dynamic gait stability at touchdown (p = 0.194, η² = 0.114) and liftoff (p = 0.122, η² = 0.139). Trunk angle significantly increased (indicating backward lean) with the front load at touchdown (p < 0.001, η² = 0.648) and liftoff (p < 0.001, η² = 0.543). No significant between-group difference was found related to the step length (p = 0.344, η² = 0.076).SignificanceCarrying a front load during walking significantly alters the trunk orientation and may change the COM-BOS kinematic relationship and, therefore, fall risk. The findings could inform the design of future studies focusing on the impact of anterior load carriage on fall risk during different locomotion.