This paper presents novel and efficient strategies to spatially adapt the amount of computational effort applied based on the local dynamics of a free surface flow, for classic weakly compressible SPH (WCSPH). Using a convenient and readily parallelizable block-based approach, different regions of the fluid are assigned differing time steps and solved at different rates to minimize computationa...

Leapfrog integration has been the method of choice in N-body simulations owing to its low computational cost for a symplectic integrator with second order accuracy. We introduce a new leapfrog integrator that allows for variable timesteps for each particle in large N-body simulations. Tests with single particles in fixed potentials show that it behaves as a symplectic integrator. We then examin...

Numerical solution of the advectionedispersion equation, used to evaluate transport of solutes in porous media, requires discretization schemes for space and time stepping. We examine use of quadratic upstream interpolation schemes QUICK, QUICKEST, and the total variation diminution scheme ULTIMATE, and compare these with UPSTREAM and CENTRAL schemes in the HYDRUS-1D model. Results for purely c...

Two fluid (TF) ideal magnetohydrodynamics (MHD) equations are a generalized form of the ideal MHD equations in which the electrons and ions are considered as separate species. The design of efficient numerical schemes for the these equations is complicated on account of the non-linearities and the presence of stiff source terms, particularly for realistic charge to mass ratios. We design novel ...

This paper constructs extrapolated implicit-explicit time stepping methods that allow one to efficiently solve problems with both stiff and nonstiff components. The proposed methods are based on Euler steps and can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method of lines framework. Implicit-explicit schemes based on extrapolation are simple to construct, ea...

This study was aimed at examining the gender and age-related differences of dynamic balance based on four stepping tests for the elderly. One hundred and eleven healthy subjects aged 60-85 were classified into four age groups (60-64, 65-69, 70-74, and 75-85) to examine age-related differences. They conducted stepping motions lasting 20-sec, including both-leg stepping right/left, both-leg stepp...

1 I n t r o d u c t i o n . This work appl ies some l inear a lgebra ideas in an o rd ina ry differential equa t ion (ODE) context . We begin by summar i s ing the a p p r o p r i a t e l inear a lgebra , and then we in t roduce the O D E problem. *Received July 1995. Revised July 1996. tThis work was supported by Engineering and Physical Sciences Research Council grants GR/H94634 and GR/KS0228...

This report introduces the “Time Stepping Package for Optimization”, or TSOpt, which is an interface for time-stepping simulation written in C++. It packages a simulator together with its derivatives (“sensitivities”) and adjoint derivatives with respect to simulation parameters in a single object called a Jet, which can be used in conjunction with an optimization algorithm to solve a simulatio...

in this paper an efficient dual time implicit approach is used to solve viscous laminar flow around two bodies with general motion. therefore, the grid includes a background grid and two sets of grids around the moving bodies. rotational and translational motions of two bodies are managed separately in this grid arrangement. in this work the overset concept for hybrid grid is used and flow vari...

In the numerical solution of partial differential equations using a method-of-lines approach, the availability of high order spatial discretization schemes motivates the development of sophisticated high order time integration methods. For multiphysics problems with both stiff and non-stiff terms implicit-explicit (IMEX) time stepping methods attempt to combine the lower cost advantage of expli...