# Application of adaptive time marching scheme in exponential basis function method in simulating solitary wave propagation

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## Abstract

Solitary wave theories are frequently adopted to simulate the characteristics of tsunami and to predict the resulting run-up in a numerical and experimental manner. A mesh-free method based on exponential basis functions (EBFs) is implemented to simulate the generation and propagation of solitary waves generated by piston-type wave maker. The pressure form of the Euler equations in a Lagrangian formulation is considered in the method. One of the most significant issues in the numerical simulation of solitary wave is to stabilize the wave height during the propagation. A new stable Lagrangian time marching algorithm is introduced which applies an adaptive parameter based on pressure formulation for tracking free surface and to minimize the discrepancies. In order to evaluate the accuracy of this newly introduced scheme, the results of EBF numerical model is applied to wave propagation according to six solitary wave theories. The results indicate the advantage of the introduced adaptive Lagrangian time marching algorithm and the EBF method in simulating solitary wave propagation with pronounced accuracy, convenient performances and the least run time calculation with implications for predicting solitary wave run-up on the beach.

## Keywords

Solitary wave Mesh-free method Pressure formulation Exponential basis functions Adaptive Lagrangian time marching## Notes

## Supplementary material

## References

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