## Solving the linear radiation problem using a volume method on an overset grid

Publication: Research - peer-review › Article in proceedings – Annual report year: 2012

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**Solving the linear radiation problem using a volume method on an overset grid.** / Read, Robert; Bingham, Harry B.

Publication: Research - peer-review › Article in proceedings – Annual report year: 2012

### Harvard

*International Workshop on Water Waves and Floating Bodies.*

### APA

*International Workshop on Water Waves and Floating Bodies.*

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### MLA

*International Workshop on Water Waves and Floating Bodies.*2012.

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### RIS

TY - GEN

T1 - Solving the linear radiation problem using a volume method on an overset grid

A1 - Read,Robert

A1 - Bingham,Harry B.

AU - Read,Robert

AU - Bingham,Harry B.

PY - 2012

Y1 - 2012

N2 - This paper describes recent progress towards the development of a computational tool, based on potential <br/>ow theory, that can accurately and effciently simulate wave-induced loadings on marine structures. Engsig-Karup et al. (2009) have successfully developed an arbitrary-order, finite-differencebased, potentialow model to represent the propagation of fully non-linear waves in coastal regions of varying bathymetry. The present objective is to develop this methodology to include the presence of a oating structure. To represent the curvilinear boundaries of the structure and the bottom, the single-block methodology developed previously is applied to multiple, overlapping grid blocks using <br/>the overset approach. While the ultimate aim of this work is to model fully non-linear wave-structure interaction, a linear solver has been initially implemented to permit the use of a fixed grid, and to allow comparison of numerical results with established analytical solutions. <br/>The linear radiation problem is considered in this paper. A two-dimensional computational tool has been developed to calculate the force applied to a floating body of arbitrary form in response to a prescribed displacement. Fourier transforms of the time-dependent displacement and force are applied, and the ratio of the resulting signals used to determine the radiation added mass and damping of the body as a function of frequency. The present software implementation has been validated by comparing numerical results from the linear model with analytical solutions for several test cases. The dynamic behaviour of a cylinder and barge on variable bathymetry has been investigated on <br/>a multi-block grid in two dimensions. Simulations have been performed to evaluate the induced flow field and radiation forces generated by these bodies in response to a Gaussian displacement. The hydrodynamic coecients associated with body motions in surge, heave, and pitch have been calculated and compared with exact solutions. A three-dimensional implementation of the linear model has recently been completed.

AB - This paper describes recent progress towards the development of a computational tool, based on potential <br/>ow theory, that can accurately and effciently simulate wave-induced loadings on marine structures. Engsig-Karup et al. (2009) have successfully developed an arbitrary-order, finite-differencebased, potentialow model to represent the propagation of fully non-linear waves in coastal regions of varying bathymetry. The present objective is to develop this methodology to include the presence of a oating structure. To represent the curvilinear boundaries of the structure and the bottom, the single-block methodology developed previously is applied to multiple, overlapping grid blocks using <br/>the overset approach. While the ultimate aim of this work is to model fully non-linear wave-structure interaction, a linear solver has been initially implemented to permit the use of a fixed grid, and to allow comparison of numerical results with established analytical solutions. <br/>The linear radiation problem is considered in this paper. A two-dimensional computational tool has been developed to calculate the force applied to a floating body of arbitrary form in response to a prescribed displacement. Fourier transforms of the time-dependent displacement and force are applied, and the ratio of the resulting signals used to determine the radiation added mass and damping of the body as a function of frequency. The present software implementation has been validated by comparing numerical results from the linear model with analytical solutions for several test cases. The dynamic behaviour of a cylinder and barge on variable bathymetry has been investigated on <br/>a multi-block grid in two dimensions. Simulations have been performed to evaluate the induced flow field and radiation forces generated by these bodies in response to a Gaussian displacement. The hydrodynamic coecients associated with body motions in surge, heave, and pitch have been calculated and compared with exact solutions. A three-dimensional implementation of the linear model has recently been completed.

BT - International Workshop on Water Waves and Floating Bodies

T2 - International Workshop on Water Waves and Floating Bodies

ER -