Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userA Stabilised Nodal Spectral Element Method for Fully Nonlinear Water Waves
134
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al (1998) cite{CaiEtAl1998}, although the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global $L^2$ projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively removes any aliasing driven instabilities while retaining the high-order accuracy of the numerical scheme. The additional computational cost of the over-integration is found insignificant compared to the cost of solving the Laplace problem. The model is applied to several benchmark cases in two dimensions. The results confirm the high order accuracy of the model (exponential convergence), and demonstrate the potential for accuracy and speedup. The results of numerical experiments are in excellent agreement with both analytical and experimental results for strongly nonlinear and irregular dispersive wave propagation. The benefit of using a high-order -- possibly adapted -- spatial discretization for accurate water wave propagation over long times and distances is particularly attractive for marine hydrodynamics applications.
rate research
Read More
We present a new stabilised and efficient high-order nodal spectral element method based on the Mixed Eulerian Lagrangian (MEL) method for general-purpose simulation of fully nonlinear water waves and wave-body interactions. In this MEL formulation a standard Laplace formulation is used to handle arbitrary body shapes using unstructured - possibly hybrid - meshes consisting of high-order curvilinear iso-parametric quadrilateral/triangular elements to represent the body surfaces and for the evolving free surface. Importantly, our numerical analysis highlights that a single top layer of quadrilaterals elements resolves temporal instabilities in the numerical MEL scheme that are known to be associated with mesh topology containing asymmetric element orderings. The surface variable only free surface formulation based on introducing a particle-following (Lagrangian) reference frame contains quartic nonlinear terms that require proper treatment by numerical discretisation due to the possibility of strong aliasing effects. We demonstrate how to stabilise this nonlinear MEL scheme using an efficient combination of (i) global L2 projection without quadrature errors, (ii) mild nonlinear spectral filtering and (iii) re-meshing techniques. Numerical experiments revisiting known benchmarks are presented, and highlights that modelling using a high-order spectral element method provides excellent accuracy in prediction of nonlinear and dispersive wave propagation, and of nonlinear wave-induced loads on fixed submerged and surface-piercing bodies.
A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a formulation of a fully nonlinear and dispersive potential flow water wave model with random inputs for the probabilistic description of the evolution of waves. The model is analyzed using random sampling techniques and non-intrusive methods based on generalized Polynomial Chaos (PC). These methods allow to accurately and efficiently estimate the probability distribution of the solution and require only the computation of the solution in different points in the parameter space, allowing for the reuse of existing simulation software. The choice of the applied methods is driven by the number of uncertain input parameters and by the fact that finding the solution of the considered model is computationally intensive. We revisit experimental benchmarks often used for validation of deterministic water wave models. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in comparison with experimental measurements could be partially explained by the variability in the model input. We finally present a synthetic experiment studying the variance based sensitivity of the wave load on an off-shore structure to a number of input uncertainties. In the numerical examples presented the PC methods have exhibited fast convergence, suggesting that the problem is amenable to being analyzed with such methods.
We present a 3D hybrid method which combines the Finite Element Method (FEM) and the Spectral Boundary Integral method (SBIM) to model nonlinear problems in unbounded domains. The flexibility of FEM is used to model the complex, heterogeneous, and nonlinear part -- such as the dynamic rupture along a fault with near fault plasticity -- and the high accuracy and computational efficiency of SBIM is used to simulate the exterior half spaces perfectly truncating all incident waves. The exact truncation allows us to greatly reduce the domain of spatial discretization compared to a traditional FEM approach, leading to considerable savings in computational cost and memory requirements. The coupling of FEM and SBIM is achieved by the exchange of traction and displacement boundary conditions at the computationally defined boundary. The method is suited to implementation on massively parallel computers. We validate the developed method by means of a benchmark problem. Three more complex examples with a low velocity fault zone, low velocity off-fault inclusion, and interaction of multiple faults, respectively, demonstrate the capability of the hybrid scheme in solving problems of very large sizes. Finally, we discuss potential applications of the hybrid method for problems in geophysics and engineering.
Spectral induced polarization (SIP) is a non-intrusive geophysical method that is widely used to detect sulfide minerals, clay minerals, metallic objects, municipal wastes, hydrocarbons, and salinity intrusion. However, SIP is a static method that cannot measure the dynamics of flow and solute/species transport in the subsurface. To capture these dynamics, the data collected with the SIP technique needs to be coupled with fluid flow and reactive-transport models. To our knowledge, currently, there is no simulator in the open-source literature that couples fluid flow, solute transport, and SIP process models to analyze geoelectrical signatures in a large-scale system. A massively parallel simulation framework (PFLOTRAN-SIP) was built to couple SIP data to fluid flow and solute transport processes. This framework built on the PFLOTRAN-E4D simulator that couples PFLOTRAN and E4D, without sacrificing computational performance. PFLOTRAN solves the coupled flow and solute transport process models to estimate solute concentrations, which were used in Archies model to compute bulk electrical conductivities at near-zero frequency. These bulk electrical conductivities were modified using the Cole-Cole model to account for frequency dependence. Using the estimated frequency-dependent bulk conductivities, E4D simulated the real and complex electrical potential signals for selected frequencies for SIP. The PFLOTRAN-SIP framework was demonstrated through a synthetic tracer-transport model simulating tracer concentration and electrical impedances for four frequencies. Later, SIP inversion estimated bulk electrical conductivities by matching electrical impedances for each specified frequency. The estimated bulk electrical conductivities were consistent with the simulated tracer concentrations from the PFLOTRAN-SIP forward model.
In marine offshore engineering, cost-efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a fully nonlinear potential flow (FNPF) model discretized using a Galerkin spectral element method to serve as a basis for handling both wave propagation and wave-body interaction with high computational efficiency within a single modellingapproach. We design and propose an efficientO(n)-scalable computational procedure based on geometric p-multigrid for solving the Laplace problem in the numerical scheme. The fluid volume and the geometric features of complex bodies is represented accurately using high-order polynomial basis functions and unstructured meshes with curvilinear prism elements. The new p-multigrid spectralelement model can take advantage of the high-order polynomial basis and thereby avoid generating a hierarchy of geometric meshes with changing number of elements as required in geometric h-multigrid approaches. We provide numerical benchmarks for the algorithmic and numerical efficiency of the iterative geometric p-multigrid solver. Results of numerical experiments are presented for wave propagation and for wave-body interaction in an advanced case for focusing design waves interacting with a FPSO. Our study shows, that the use of iterative geometric p-multigrid methods for theLaplace problem can significantly improve run-time efficiency of FNPF simulators.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
