In this note, we apply the h-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic partial differential equations, with the objective of ach...In this note, we apply the h-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic partial differential equations, with the objective of achieving high order accuracy and mesh efficiency. We compute the numerical solution to a steady state Burgers equation and the solution to a converging-diverging nozzle problem. The computational results verify that, by suitably choosing the artificial viscosity coefficient and applying the adaptive strategy based on a posterior error estimate by Johnson et al., an order of N^-3/2 accuracy can be obtained when continuous piecewise linear elements are used, where N is the number of elements.展开更多
In this paper I review three key topics in CFD that have kept researchers busy for half a century.First,the concept of upwind differencing,evident for 1-D linear advection.Second,its implementation for nonlinear syste...In this paper I review three key topics in CFD that have kept researchers busy for half a century.First,the concept of upwind differencing,evident for 1-D linear advection.Second,its implementation for nonlinear systems in the form of highresolution schemes,now regarded as classical.Third,its genuinely multidimensional implementation in the form of residual-distribution schemes,the most recent addition.This lecture focuses on historical developments;it is not intended as a technical review of methods,hence the lack of formulas and absence of figures.展开更多
文摘In this note, we apply the h-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic partial differential equations, with the objective of achieving high order accuracy and mesh efficiency. We compute the numerical solution to a steady state Burgers equation and the solution to a converging-diverging nozzle problem. The computational results verify that, by suitably choosing the artificial viscosity coefficient and applying the adaptive strategy based on a posterior error estimate by Johnson et al., an order of N^-3/2 accuracy can be obtained when continuous piecewise linear elements are used, where N is the number of elements.
文摘In this paper I review three key topics in CFD that have kept researchers busy for half a century.First,the concept of upwind differencing,evident for 1-D linear advection.Second,its implementation for nonlinear systems in the form of highresolution schemes,now regarded as classical.Third,its genuinely multidimensional implementation in the form of residual-distribution schemes,the most recent addition.This lecture focuses on historical developments;it is not intended as a technical review of methods,hence the lack of formulas and absence of figures.
