In estuaries, the part of a river where the flow is predominantly driven by the tide, the water motion is important to understand. For instance, by understanding the flow, one can better predict how pollutants are transported, or when flooding is likely to occur. However, much is still unknown about certain aspects of the water motion, such as how the hydrodynamics are influenced by the steepness of the river bed.

In this thesis, the effect of steep lateral inclines on the river bed is systematically investigated. Because these steep inclines come with significant mathematical challenges, a new model for the water motion in estuaries is developed.

To study the effects of steepness, the model is applied to short estuaries with increasingly deep channels with increasingly steep inclines in the middle of the river, and shallower waters closer to the banks. The results indicate that during flood, i.e. the moment when flow into the estuary is strongest, water flows in through the deep channel and then from the channel towards the banks. During ebb, this pattern is reversed. For estuaries with steeper beds, currents are stronger, and the previously mentioned pattern is more pronounced.

Through a process known as momentum advection, so-called residual currents appear that are present regardless of the phase of the tidal cycle. Because these residual currents produce net transport by the movement of water, they are crucial in many transport processes involving sand, mud, salt, pollutants or other materials. The structure of the current is as follows: in the deeper channels, the residual current flows from the sea into the channel, and close to the banks,water flows out of the estuary. Steeper beds cause the residual flow to become stronger and (indirectly) because of the Coriolis effect, notably asymmetric.

Voxels are cells on a 3D regular grid. Voxel-based scenes have many applications, including frequent use in simulations or games. Over the years, the field of high-resolution voxel scenes has progressed significantly, allowing for compressing and real-time editing of high-resolution scenes. This possibility of editing high-resolution scenes led to various editing tools. This thesis aims to expand this set of tools with a focus on more complex simulation-based solutions. We explored the field of terrain weathering and decided on a spheroidal weathering tool to perform weathering on voxel-based scenes. One of the existing limitations of this particular method was that it did not account for debris simulation. We ultimately decided to add a granular simulation using a layer-based approach that integrates with the weathering tool but is also able to function in a standalone manner.
This thesis presents three highly-customizable editing tools for voxel-based scenes: spheroidal weathering, granular simulation, and a combined tool that enables weathering with debris simulation. These tools are integrated into the HashDAG framework, which is a high-resolution voxel-grid method building upon a directed acyclic graph representation of a sparse voxel octree. Our solutions enable close to real-time editing for changes with a smaller regional support. There is room for improvement in terms of performance at scale, with various potential ideas presented in the future work section.

The goal of seismic imaging is to create a model of the subsurface from samples of a transmitted wavefield that is reflected in soil layers.
The created model can be used to locate storage possibilities for CO2 or H2 or to find oil and gas reservoirs or other natural resources.
Seismic imaging relies on the propagation of wavefields, which can be computed by evaluating the Rayleigh integral, a process that often requires a lot of time and resources.
In this thesis we develop methods to reduce error in the computation of the Rayleigh integral whilst remaining time-efficient.
To achieve this we first give the derivation of the Rayleigh integral and provide a few methods to evaluate integrals numerically using interpolating polynomials.
Afterwards, we adapt the integration methods to the Rayleigh integral and arrive at the main algorithms for its evaluation, at the end we compare these algorithms.

We present the method that is currently used for the computation of the Rayleigh integral and a modification that extends the method to samples on a rectilinear grid.
The adjusted version of this method did not perform consistently in our results, although it achieved better results than the original method on average.
Secondly we present a combined interpolation method (that is, it interpolates the full integrand without taking advantage that one of the two functions in the integrand is known) named Simpson's rule, which only performed better in the high sample points per wavelength range with minimal noise.
An alteration to the method for semi-equidistant grids also did not perform consistently and is not worth the extra operations.
Next was the separate interpolation algorithm (this time taking advantage of the known part of the integrand), this method is difficult to implement and had only slightly better performance than the combined method.
The final method was an extension of the separate interpolation algorithm to non-equidistant grids, this method performed undoubtedly the best of all presented methods (often better by a factor of 15 compared to the currently used method), this method is therefore recommended for evaluating the Rayleigh integral.
The amount of operations needed for all presented methods is approximately the same and the execution time needed for the calculation depends on the implementation of the problem.

In conclusion, we found that the separate interpolation method for non-equidistant grids delivered the most accurate approximations of the Rayleigh integral. This method can be used in seismic imaging to increase the accuracy of models of the subsurface.

Computational Fluid Dynamics (CFD) is the main tool to use in industry and engineering problems including turbulent flows. Turbulence modeling relies on solving the Navier-Stokes equations. Solving these equations directly takes a lot of time and computational power. More affordable methods solve the Reynolds Averaged Navier-Stokes (RANS) equations.
The most commonly used RANS models rely on Linear Eddy Viscosity Models for the Reynolds stress closure. However, this type of modeling does not provide satisfactory accuracy in general problems, which include curvature, impingement and separation. The rapid developments of Machine Learning (ML) in fluid dynamics and the increase of available high fidelity data of turbulent flows led to the introduction of data-driven RANS turbulence modeling. ML-augmented RANS models are promising but often lack generalisability or does not meet the preference of being interpretable. In this thesis, a sparse symbolic regression method has been used to generate interpretable algebraic equations for the non linear anisotropic Reynolds stress. These equations are built from a library of candidate functions of which the best fitting functions are selected by solving a sparse regression problem.
A deeper understanding of this methodology is achieved by creating models using different input features, including a wall damping function to improve near-wall behaviour of the model. Furthermore, different sparse regression problems are investigated, including constrained regression problems for which physical knowledge is used. The discovered models are propagated in a CFD solver to obtain a corrected velocity field.
Most of the discovered models improve the prediction of the Reynolds stress and its anisotropy compared to the $k-\omega$ RANS model. A small number of the discovered models are able to improve the prediction of the streamwise velocity compared to the RANS model. By analysing the discovered models, it is recognised that a specific term in the algebraic model is the basis of an inadequate prediction of the velocity. Furthermore, it is observed that a considerable amount of the implemented models provide an unconverged solution, which is visible as instabilities in the flow variables. Suggestions are given to improve the stability of the models. The discovered models, which include more physical knowledge by applying physical constraints to the regression problem or by including near-wall treatments, give promising results.

Numerical methods for solving problems with a large contrast in the coefficients are investigated in this report. These types of problems typically appear in basin modeling. Specifically, the deflation and restricted additive Schwarz (RAS) methods are compared for their effectiveness in solving this type of problem in combination with the conjugate gradient method, both in terms of iterations and computation time. It is shown that the RAS method converges to the correct solution in a small amount of iterations. However, the deflation method, in combination with another preconditioner, performs better in terms of computation time. An important observation is that the relative residual can only be used as a reliable stopping criterion when the deflation method is used. The methods can be combined into the DRASCG method, which converges in an extremely small number of iterations. In a parallel environment, the speedup of the RASCG method is limited by a load imbalance in the amount of work required for the application of the preconditioner for each subdomain. The deflation method obtains good speedup, that is close to the ideal speedup. The methods are compared when the number of subdomains is increased. It is shown that a classic data distribution is not effective for this type of problem. The deflation method is shown to be robust for a physics based domain decomposition.

Using an idealized width-averaged model, the influence of spring-neap cycles on the transport and trapping of suspended fine sediment in tide-dominated estuaries is investigated. To this end we introduce a multiple time scale expansion. This provides a mathematically sound argument for treating the fast ebb-flood cycle and the slow spring-neap variations as independent time scales. With this expansion, semi-analytical approximations of the water motion and suspended sediment concentrations can be found as functions of the spring-neap time scale. The advantage of this is that the transport of sediment is then investigated in a tidally-averaged sense using analytically obtained temporal dependencies and model simulations based on the conditions in 2005 of the Ems-Dollard estuary. We found that sediment import is strongly enhanced during spring tide and that a combination of vanishing import processes and sediment export due to river discharge resulted in a net export of sediment during neap tide. Furthermore the spring-neap varying deposition of fine sediment in a bottom pool on the river bed is investigated. We found that the time needed for the system to adjust to new equilibrium conditions can not be neglected within a spring-neap cycle as temporal lag effects are clearly visible in the dynamic behaviour of the bottom pool and suspended sediment concentrations. These temporal lag effects are sensitive to the choice of the parameter governing erosion. Assuming different values of the erosion parameter we have shown that the long-term characteristics of the bottom pool are sensitive to these temporal lag effects. Choosing a low value of the erosion parameter results in the presence of a bottom pool throughout the spring-neap cycle. With a high value of the erosion no bottom pool is formed at any time in the spring-neap cycle.