Very High-Order Accurate Sharp Immersed Interface Method: Application to Direct Numerical Simulations of Incompressible Flows

2017 ◽  
Author(s):  
Shirzad Hosseinverdi ◽  
Hermann F. Fasel
Keyword(s):  
Numerical Simulations ◽  
Incompressible Flows ◽  
High Order ◽  
Direct Numerical Simulations ◽  
Immersed Interface Method ◽  
Immersed Interface ◽  
Very High

scholarly journals Direct numerical simulations of helical dynamo action: MHD and beyond

2004 ◽  
Vol 11 (5/6) ◽  
pp. 619-629 ◽  
Author(s):  
D. O. Gómez ◽  
P. D. Mininni
Keyword(s):  
Magnetic Fields ◽  
Numerical Simulations ◽  
Periodic Boundary ◽  
Incompressible Flows ◽  
Magnetic Energy ◽  
Periodic Boundary Conditions ◽  
Direct Numerical Simulations ◽  
Dynamo Action ◽  
Spatial Fluctuations ◽  
Kinetic Effects

Abstract. Magnetohydrodynamic dynamo action is often invoked to explain the existence of magnetic fields in several astronomical objects. In this work, we present direct numerical simulations of MHD helical dynamos, to study the exponential growth and saturation of magnetic fields. Simulations are made within the framework of incompressible flows and using periodic boundary conditions. The statistical properties of the flow are studied, and it is found that its helicity displays strong spatial fluctuations. Regions with large kinetic helicity are also strongly concentrated in space, forming elongated structures. In dynamo simulations using these flows, we found that the growth rate and the saturation level of magnetic energy and magnetic helicity reach an asymptotic value as the Reynolds number is increased. Finally, extensions of the MHD theory to include kinetic effects relevant in astrophysical environments are discussed.

scholarly journals New Finite Difference Methods Based on IIM for Inextensible Interfaces in Incompressible Flows

2011 ◽  
Vol 1 (2) ◽  
pp. 155-171 ◽  
Author(s):  
Zhilin Li ◽  
Ming-Chih Lai
Keyword(s):  
Surface Tension ◽  
Finite Difference ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Finite Difference Methods ◽  
Navier Stokes ◽  
Immersed Interface Method ◽  
Immersed Interface ◽  
Navier Stokes Equations ◽  
Difference Methods

AbstractIn this paper, new finite difference methods based on the augmented immersed interface method (IIM) are proposed for simulating an inextensible moving interface in an incompressible two-dimensional flow. The mathematical models arise from studying the deformation of red blood cells in mathematical biology. The governing equations are incompressible Stokes or Navier-Stokes equations with an unknown surface tension, which should be determined in such a way that the surface divergence of the velocity is zero along the interface. Thus, the area enclosed by the interface and the total length of the interface should be conserved during the evolution process. Because of the nonlinear and coupling nature of the problem, direct discretization by applying the immersed boundary or immersed interface method yields complex nonlinear systems to be solved. In our new methods, we treat the unknown surface tension as an augmented variable so that the augmented IIM can be applied. Since finding the unknown surface tension is essentially an inverse problem that is sensitive to perturbations, our regularization strategy is to introduce a controlled tangential force along the interface, which leads to a least squares problem. For Stokes equations, the forward solver at one time level involves solving three Poisson equations with an interface. For Navier-Stokes equations, we propose a modified projection method that can enforce the pressure jump condition corresponding directly to the unknown surface tension. Several numerical experiments show good agreement with other results in the literature and reveal some interesting phenomena.

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