The work proposes a model of biological fluid flow in a steady mode through a cylindrical layer taking into account convection and diffusion.The model considers finite compressibility and concentration expansion conne...The work proposes a model of biological fluid flow in a steady mode through a cylindrical layer taking into account convection and diffusion.The model considers finite compressibility and concentration expansion connected with both barodiffusion and additional mechanism of pressure change in the pore volume due to the concentration gradient.Thus,the model is entirely coupled.The paper highlights the complexes composed of scales of physical quantities of different natures.The iteration algorithm for the numerical solution of the problem was developed for the coupled problem.The work involves numerical studies of the considered effects on the characteristics of the flow that can be convective or diffusive,depending on the relation between the dimensionless complexes.It is demonstrated that the distribution of velocity and concentration for different cylinder wall thicknesses is different.It is established that the barodiffusion has a considerable impact on the process in the convective mode or in the case of reduced cylinder wall thickness.展开更多
This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual ...This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta condition holds. Then, based on these structure properties, the wellposedness close to a constant state can be proved by using fine energy estimates. The asymptotic decay of the solutions are also investigated.展开更多
The computation of the radiative transfer equation is expensive mainly due to two stiff terms:the transport term and the collision operator.The stiffness in the former comes from the fact that particles(such as photon...The computation of the radiative transfer equation is expensive mainly due to two stiff terms:the transport term and the collision operator.The stiffness in the former comes from the fact that particles(such as photons)travel at the speed of light,while that in the latter is due to the strong scattering in the optically thick region.We study the fully implicit scheme for this equation to account for the stiffness.The main challenge in the implicit treatment is the coupling between the spacial and angular coordinates that requires the large size of the to-be-inverted matrix,which is also ill-conditioned and not necessarily symmetric.Our main idea is to utilize the spectral structure of the ill-conditioned matrix to construct a pre-conditioner,which,along with an exquisite split of the spatial and angular dependence,significantly improve the condition number and allows a matrix-free treatment.We also design a fast solver to compute this pre-conditioner explicitly in advance.Our method is shown to be efficient in both diffusive and free streaming limit,and the computational cost is comparable to the state-of-the-art method.Various examples including anisotropic scattering and two-dimensional problems are provided to validate the effectiveness of our method.展开更多
This work develops near-optimal controls for systems given by differential equations with wideband noise and random switching.The random switching is modeled by a continuous-time,time-inhomogeneous Markov chain.Under ...This work develops near-optimal controls for systems given by differential equations with wideband noise and random switching.The random switching is modeled by a continuous-time,time-inhomogeneous Markov chain.Under broad conditions,it is shown that there is an associated limit problem,which is a switching jump diffusion.Using near-optimal controls of the limit system,we then build controls for the original systems.It is shown that such constructed controls are nearly optimal.展开更多
基金the Government Research Assignment for ISPMS SB RAS,project FWRW-2021-0007.Author information。
文摘The work proposes a model of biological fluid flow in a steady mode through a cylindrical layer taking into account convection and diffusion.The model considers finite compressibility and concentration expansion connected with both barodiffusion and additional mechanism of pressure change in the pore volume due to the concentration gradient.Thus,the model is entirely coupled.The paper highlights the complexes composed of scales of physical quantities of different natures.The iteration algorithm for the numerical solution of the problem was developed for the coupled problem.The work involves numerical studies of the considered effects on the characteristics of the flow that can be convective or diffusive,depending on the relation between the dimensionless complexes.It is demonstrated that the distribution of velocity and concentration for different cylinder wall thicknesses is different.It is established that the barodiffusion has a considerable impact on the process in the convective mode or in the case of reduced cylinder wall thickness.
基金Project supported by the Fundamental Research Funds for the Central Universities (No. 2009B27514)the National Natural Science Foundation of China (No. 10871059)
文摘This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta condition holds. Then, based on these structure properties, the wellposedness close to a constant state can be proved by using fine energy estimates. The asymptotic decay of the solutions are also investigated.
基金The work of Q.Li is supported in part by a start-up fund from UW-Madison and National Science Foundation under the grant DMS-1619778The work of L.Wang is supported in part by the National Science Foundation under the grant DMS-1620135Both authors would like to express gratitude to the support from the NSF research network grant RNMS11-07444(KI-Net).We also thank Professors Shi Jin,Jim Morel and Cory Hauck for fruitful discussions.
文摘The computation of the radiative transfer equation is expensive mainly due to two stiff terms:the transport term and the collision operator.The stiffness in the former comes from the fact that particles(such as photons)travel at the speed of light,while that in the latter is due to the strong scattering in the optically thick region.We study the fully implicit scheme for this equation to account for the stiffness.The main challenge in the implicit treatment is the coupling between the spacial and angular coordinates that requires the large size of the to-be-inverted matrix,which is also ill-conditioned and not necessarily symmetric.Our main idea is to utilize the spectral structure of the ill-conditioned matrix to construct a pre-conditioner,which,along with an exquisite split of the spatial and angular dependence,significantly improve the condition number and allows a matrix-free treatment.We also design a fast solver to compute this pre-conditioner explicitly in advance.Our method is shown to be efficient in both diffusive and free streaming limit,and the computational cost is comparable to the state-of-the-art method.Various examples including anisotropic scattering and two-dimensional problems are provided to validate the effectiveness of our method.
基金supported in part by the National Science Foundation under DMS-1207667supported in part by NSFC and RFDP
文摘This work develops near-optimal controls for systems given by differential equations with wideband noise and random switching.The random switching is modeled by a continuous-time,time-inhomogeneous Markov chain.Under broad conditions,it is shown that there is an associated limit problem,which is a switching jump diffusion.Using near-optimal controls of the limit system,we then build controls for the original systems.It is shown that such constructed controls are nearly optimal.
