Abstract
SummaryMultiphase inertia‐dominated flow simulations, and free surface flow models in particular, continue to this day to present many challenges in terms of accuracy and computational cost to industry and research communities. Numerical wave tanks and their use for studying wave‐structure interactions are a good example. Finite element method (FEM) with anisotropic meshes combined with dynamic mesh algorithms has already shown the potential to significantly reduce the number of elements and simulation time with no accuracy loss. However, mesh anisotropy can lead to mesh quality‐related instabilities. This article presents a very robust FEM approach based on a control volume discretization of the pressure field for inertia dominated flows, which can overcome the typically encountered mesh quality limitations associated with extremely anisotropic elements. Highly compressive methods for the water‐air interface are used here. The combination of these methods is validated with multiphase free surface flow benchmark cases, showing very good agreement with experiments even for extremely anisotropic meshes, reducing by up to two orders of magnitude the required number of elements to obtain accurate solutions.
Highlights
Studying wave-structure interaction (WSI) with numerical wave tanks (NWTs) has become common practice for research institutions and for industry, complementing and sometimes replacing physical modeling and empirical formulas as design tools
The novel P1DGP1(CV) scheme is proven to be as accurate as P1DGP1 standard CVFEM scheme, while being more robust and capable of resolving free surface flow problems with highly anisotropic meshes accurately
These code developments when applied to NWTs effectively accelerate Finite element method (FEM) approaches with their typical higher accuracy, when compared to generally established faster NWTs based on finite volumes method (FVM) or SPH alternatives.[40,41,42]
Summary
Studying wave-structure interaction (WSI) with numerical wave tanks (NWTs) has become common practice for research institutions and for industry, complementing and sometimes replacing physical modeling and empirical formulas as design tools. Dynamic mesh optimization (DMO) schemes can be used in order to significantly reduce computational cost without losing accuracy by adapting the mesh at different time steps.[6,7,8,9,10,11,12] This is attractive for multiphase problems where the air-water interface can be resolved with a moving high-resolution anisotropic mesh, such NWTs. Using highly optimized anisotropic meshes can often lead to elements with large angles, which can make the model take significantly longer (creating matrices that are difficult to solve) or even fail to converge.[13,14] DMO could be deemed impractical when highly anisotropic meshes are required if these are seen to be associated with model instability. This article proposes using a novel P1DGP1(CV), discretizing with CVs, the pressure field, and with DG of order 1, the critical velocity field This has the potential to add stability and robustness to the classical P1DGP1 when using highly anisotropic meshes and DMO for computational cost optimization.
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