An h-adaptive method is developed for high-order discontinuous Galerkin methods(DGM)to solve the laminar compressible Navier-Stokes(N-S)equations on unstructured mesh.The vorticity is regarded as the indicator of adap...An h-adaptive method is developed for high-order discontinuous Galerkin methods(DGM)to solve the laminar compressible Navier-Stokes(N-S)equations on unstructured mesh.The vorticity is regarded as the indicator of adaptivity.The elements where the vorticity is larger than a pre-defined upper limit are refined,and those where the vorticity is smaller than a pre-defined lower limit are coarsened if they have been refined.A high-order geometric approximation of curved boundaries is adopted to ensure the accuracy.Numerical results indicate that highly accurate numerical results can be obtained with the adaptive method at relatively low expense.展开更多
We present an adaptive lattice Boltzmann model to simulate super- sonic flows.The particle velocities are determined by the mean velocity and internal energy.The adaptive nature of particle velocities permits the mean...We present an adaptive lattice Boltzmann model to simulate super- sonic flows.The particle velocities are determined by the mean velocity and internal energy.The adaptive nature of particle velocities permits the mean flow to have high Mach number.A particle potential energy is introduced so that the model is suitable for the perfect gas with arbitrary specific heat ratio.The Navier-Stokes equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation. As preliminary tests,two kinds of simulations have been performed on hexagonal lattices.One is the one-dimensional simulation for sinusoidal velocity distributions. The velocity distributions are compared with the analytical solution and the mea- sured viscosity is compared with the theoretical values.The agreements are basically good.However,the discretion error may cause some non-isotropic effects.The other simulation is the 29 degree shock reflection.展开更多
基金supported by the National Natural Science Foundation of China(11272152)
文摘An h-adaptive method is developed for high-order discontinuous Galerkin methods(DGM)to solve the laminar compressible Navier-Stokes(N-S)equations on unstructured mesh.The vorticity is regarded as the indicator of adaptivity.The elements where the vorticity is larger than a pre-defined upper limit are refined,and those where the vorticity is smaller than a pre-defined lower limit are coarsened if they have been refined.A high-order geometric approximation of curved boundaries is adopted to ensure the accuracy.Numerical results indicate that highly accurate numerical results can be obtained with the adaptive method at relatively low expense.
基金The project supported by the National Natural Science Foundation of China(Grant Nos.19672030 and 19972037)and by the Scientific Research Foundation for Returned Overseas Chinese ScholarsState Education Ministry
文摘We present an adaptive lattice Boltzmann model to simulate super- sonic flows.The particle velocities are determined by the mean velocity and internal energy.The adaptive nature of particle velocities permits the mean flow to have high Mach number.A particle potential energy is introduced so that the model is suitable for the perfect gas with arbitrary specific heat ratio.The Navier-Stokes equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation. As preliminary tests,two kinds of simulations have been performed on hexagonal lattices.One is the one-dimensional simulation for sinusoidal velocity distributions. The velocity distributions are compared with the analytical solution and the mea- sured viscosity is compared with the theoretical values.The agreements are basically good.However,the discretion error may cause some non-isotropic effects.The other simulation is the 29 degree shock reflection.
