Abstract
We present a Runge–Kutta discontinuous Galerkin method for solving conservative reinitialization in the context of the conservative level set method [18,19]. This represents an extension of the method recently proposed by Owkes and Desjardins [21], by solving the level set equations on the refined level set grid [9] and projecting all spatially-dependent variables into the full basis used by the discontinuous Galerkin discretization. By doing so, we achieve the full k+1 order convergence rate in the L1 norm of the level set field predicted for RKDG methods given kth degree basis functions when the level set profile thickness is held constant with grid refinement. Shape and volume errors for the 0.5-contour of the level set, on the other hand, are found to converge between first and second order. We show a variety of test results, including the method of manufactured solutions, reinitialization of a circle and sphere, Zalesak's disk, and deforming columns and spheres, all showing substantial improvements over the high-order finite difference traditional level set method studied for example by Herrmann [9]. We also demonstrate the need for kth order accurate normal vectors, as lower order normals are found to degrade the convergence rate of the method.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 453-473 |
| Number of pages | 21 |
| Journal | Journal of Computational Physics |
| Volume | 349 |
| DOIs | |
| State | Published - Nov 15 2017 |
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Keywords
- Arbitrary order
- Conservative level set
- Discontinuous Galerkin
- Multiphase flow
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)
- Computer Science Applications
Cite this
An arbitrary-order Runge–Kutta discontinuous Galerkin approach to reinitialization for banded conservative level sets. / Jibben, Z.; Herrmann, Marcus.
In: Journal of Computational Physics, Vol. 349, 15.11.2017, p. 453-473.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An arbitrary-order Runge–Kutta discontinuous Galerkin approach to reinitialization for banded conservative level sets
AU - Jibben, Z.
AU - Herrmann, Marcus
PY - 2017/11/15
Y1 - 2017/11/15
N2 - We present a Runge–Kutta discontinuous Galerkin method for solving conservative reinitialization in the context of the conservative level set method [18,19]. This represents an extension of the method recently proposed by Owkes and Desjardins [21], by solving the level set equations on the refined level set grid [9] and projecting all spatially-dependent variables into the full basis used by the discontinuous Galerkin discretization. By doing so, we achieve the full k+1 order convergence rate in the L1 norm of the level set field predicted for RKDG methods given kth degree basis functions when the level set profile thickness is held constant with grid refinement. Shape and volume errors for the 0.5-contour of the level set, on the other hand, are found to converge between first and second order. We show a variety of test results, including the method of manufactured solutions, reinitialization of a circle and sphere, Zalesak's disk, and deforming columns and spheres, all showing substantial improvements over the high-order finite difference traditional level set method studied for example by Herrmann [9]. We also demonstrate the need for kth order accurate normal vectors, as lower order normals are found to degrade the convergence rate of the method.
AB - We present a Runge–Kutta discontinuous Galerkin method for solving conservative reinitialization in the context of the conservative level set method [18,19]. This represents an extension of the method recently proposed by Owkes and Desjardins [21], by solving the level set equations on the refined level set grid [9] and projecting all spatially-dependent variables into the full basis used by the discontinuous Galerkin discretization. By doing so, we achieve the full k+1 order convergence rate in the L1 norm of the level set field predicted for RKDG methods given kth degree basis functions when the level set profile thickness is held constant with grid refinement. Shape and volume errors for the 0.5-contour of the level set, on the other hand, are found to converge between first and second order. We show a variety of test results, including the method of manufactured solutions, reinitialization of a circle and sphere, Zalesak's disk, and deforming columns and spheres, all showing substantial improvements over the high-order finite difference traditional level set method studied for example by Herrmann [9]. We also demonstrate the need for kth order accurate normal vectors, as lower order normals are found to degrade the convergence rate of the method.
KW - Arbitrary order
KW - Conservative level set
KW - Discontinuous Galerkin
KW - Multiphase flow
UR - http://www.scopus.com/inward/record.url?scp=85028561312&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85028561312&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2017.08.035
DO - 10.1016/j.jcp.2017.08.035
M3 - Article
VL - 349
SP - 453
EP - 473
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
ER -