二阶BDF2压力修正投影方法求解扩散Peterlin粘弹性流体
Second Order BDF2 Pressure Correction Projection Method Solving Diffusive Peterlin Viscoelastic Fluid
摘要: 不可压扩散粘弹性流体是用来描述高分子聚合物的一类复杂流体。本文用二阶BDF2时间离散的压力修正投影方法求解扩散peterlin粘弹性流体。BDF2是三步格式，具有2阶收敛精度。压力修正投影方法用来避开流体速度和压力的耦合的不可压约束条件∇-u=0。当时间步长Δt小于给定常数时，我们证明了该方法无条件稳定。最后数值算例验证了格式的稳定性。
Abstract: The incompressible peterlin diffusive viscoelastic fluid is one type of complex fluid which used to describe high-molecular polymer. Second order time discrete BDF2 pressure correction projection method is to solve the diffusive peterlin viscoelastic model in this paper. BDF2 is three step steps scheme, and it has second order accuracy. Pressure correction projection method is used to avoid the incompressible restriction ∇-u=0 between the fulid velocity u and the pressure p. We prove that the method is unconditional stability if time step Δt less than a constant. Finally, we present some numerical experiment to verify the stability.
文章引用：展攀, 张运章, 梁海婷, 程嘉敏, 周欣欣, 袁晓君. 二阶BDF2压力修正投影方法求解扩散Peterlin粘弹性流体[J]. 应用数学进展, 2019, 8(6): 1051-1057. https://doi.org/10.12677/AAM.2019.86120

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