Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Motivated by providing ll-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in 2 to space discretizations. Therein studies re carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods re shown asymptotic-preserving. ,  focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-order accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are ll qualified for both non-equilibrium and equilibrium radiation diffusion. Provide AP fully discrete schemes for non-equilibrium radiation diffusion.Propose second order accurate schemes by asymmetric approach for boundary flux-limiter.Show first order AP property of spatially and fully discrete schemes with IB evolution.Devise subtle artificial solutions; verify accuracy and AP property quantitatively.Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.
['Xia Cui', 'Guangwei Yuan', 'Zhijun Shen']
I am writing a research paper on a idea Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion
[{"from": "human", "value": "I am writing a research paper on a idea Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Motivated by providing ll-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in 2 to space discretizations. Therein studies re carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods re shown asymptotic-preserving. ,  focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-order accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are ll qualified for both non-equilibrium and equilibrium radiation diffusion. Provide AP fully discrete schemes for non-equilibrium radiation diffusion.Propose second order accurate schemes by asymmetric approach for boundary flux-limiter.Show first order AP property of spatially and fully discrete schemes with IB evolution.Devise subtle artificial solutions; verify accuracy and AP property quantitatively.Ideas can be generalized to 3-dimensional problems and higher order implicit schemes."}]