A stabilized separation of variables method for the modified biharmonic equation. The modified biharmonic equation is encountered in a variety of application areas, including streamfunction formulations of the Navier-Stokes equations. We develop a separation of variables representation for this equation in polar coordinates, for either the interior or exterior of a disk, and derive a new class of special functions which makes the approach stable. We discuss how these functions can be used in conjunction with fast algorithms to accelerate the solution of the modified biharmonic equation or the ”bi-Helmholtz” equation in more complex geometries.
Keywords for this software
References in zbMATH (referenced in 4 articles , 1 standard article )
Showing results 1 to 4 of 4.
- af Klinteberg, Ludvig; Askham, Travis; Kropinski, Mary Catherine: A fast integral equation method for the two-dimensional Navier-Stokes equations (2020)
- Lei, M.; Sam, C. N.; Hon, Y. C.: Generalized finite integration method with Volterra operator for multi-dimensional biharmonic equations (2020)
- Askham, T.: A stabilized separation of variables method for the modified biharmonic equation (2018)
- Helsing, Johan; Jiang, Shidong: On integral equation methods for the first Dirichlet problem of the biharmonic and modified biharmonic equations in nonsmooth domains (2018)