Liquefaction is the phenomena when there is loss of strength in saturated and cohesion-less soils because of increased pore water pressures and hence reduced effective stresses due to dynamic loading. It is a phenomenon in which the strength and stiffness of a soil is reduced by earthquake shaking or other rapid loading. In this study, after the short review of liquefaction definition, the models of prediction and estimation of liquefaction were considered. Application of numerical modelling with two major software (FLAC & PLAXIS) for the Wildlife site liquefaction, under superstition earthquake in 1987 were compared and analysed. Third step was started with introduction of Fuzzy logic and neural network as two common intelligent mathematical methods. These two patterns for prediction of soil liquefaction were combined. The “Neural network- Fuzzy logic-Liquefaction- Prediction” (NFLP) was applied for liquefaction prediction in Wildlife site. The results show the powerful prediction of liquefaction happening with high degree of accuracy in this case.

Recently observed cumulation of unexpected collapses of slope-distant waste dumps in lignite mining areas of eastern germany re-initiated research of soil liquefaction. Especially it turned the question of internal initials that correspond to water rise. Parallel to laboritory tests and field experiments a micromechanical model should be developed, which can reproduce processes in the soil during saturation. In first approximation a partly saturated soil consists of two phases: the soil particles and the pore fluid. For micromechanical modeling a coupling of discontinuum particles) and continuum (fluid) is required. The soil particles can be simulated with the Discrete-Element-Method (DEM). For the pore fluid, which is assumed to be a mixture of liquid and gaseous fractions, Pore scale model with Finite Volumes (PFV) is used. At low water content liquid bridges (meniscii) arise between the particles that cause an apparent cohesion. The effect of the meniscii is considered by a correspondingly contact law in the DEM model. During the saturation of a soil both, cohesive effect and fluid bulk modulus, are reduced. In addition buoyancy acts on the particles during the process. The micromechanical modeling approach has the advantage, that just a few model parameters are needed. The numerical model shows pore fluid pressures during saturation process, that leads to a reduction of effective stress. It is investigated how much the reduction is regarding porosity, degree of saturation, stress conditions and grain shape. Furthermore the influence of model parameters as well as hydromechanics is investigated. The investigations are completed with another series of experiments under special conditions like integration of macropores, horizontal fixed model boundaries and abrupt saturation.:Einleitung Literaturauswertung Numerische Modellierung Modellstudien Ergebnisauswertung Zusammenfassung Extended summary

The aim of this research work is to deepen the understanding of joint shear behavior under different boundary conditions. For this purpose, joint closure tests under quasi-static and dynamic conditions, direct shear and cyclic shear tests under CNL and DNL boundary conditions of plane joints are performed using GS-1000 big shear box device. The dissertation also presents the procedure to simulate the shear box device and simulating the behavior of plane joints at the micro-scale using FLAC3D. Special attention has been given to understand the influencing factors of the normal stress level, direct shear rate, horizontal cyclic shear frequency, normal impact frequency, horizontal cyclic shear displacement amplitude and vertical impact force amplitude. Lab test and numerical simulation results show that the quasi-static joint stiffness increases with increasing normal force. Dynamic joint stiffness decreases with increasing superimposed normal force amplitudes. Normal impact frequencies have little influence on the joint stiffness. Rotations and stress changes at the plane joint during shearing are proven. Rotations and development of stress gradients can be decreased significantly by increasing the size of the bottom specimen and applying a shear velocity at the upper shear box and normal loading piston. Furthermore, peak shear force increases with increasing normal force. Friction angle of cyclic shear tests is smaller than that of direct shear tests. Moreover, significant time shifts between normal and shear force (shear force delay), normal force and friction coefficient (friction coefficient delay) during direct shear tests under DNL boundary conditions are observed and the reference quantity ‘shear-velocity-normal-impact-frequency’ (SV-NIF) to describe the behavior under DNL boundary conditions is defined. Peak shear force and minimum friction coefficient increase with increasing SV-NIF. Relative time shift between normal force and shear force decreases with increase of SV-NIF. The mechanical behavior of the GS-1000 big shear box device is simulated and the loss of normal force caused by the tilting of the loading plate is quantified. Finally, the novel direct and cyclic shear strength criterions under DNL conditions are put forward. The shear strength criterions are in close agreement with the measured values, which indicates that the novel shear strength criterions are able to predict the shear strength under DNL conditions.

The presented work documents the influence of Voronoi block size and shape as well as internal mesh size on the calibrated fracture toughness KIC. It is documented that Voronoi based procedures have an inevitable error of up to ± 30%. On the other hand, this approach is able to reproduce complex fracture pattern in a realistic manner with reasonable computational power. The work propose a KIC calibration procedure and documents based on the comparison with lab tests, that crack propagation, fracture pattern as well as stress-strain behavior of brittle solids can be duplicated by calibrated Voronoi based DEM simulations. The thesis also documents a swelling law for the DEM code UDEC including parameter determination and validation on lab tests with swelling cement. Finally, calibrated concrete models with one or two holes under different boundary conditions are used to predict swelling induced cracking. Numerical predictions were compared with corresponding lab tests and showed satisfying results.

This study presents numerical modeling of geologic processes based on Discrete Element Method (DEM), including modeling of pull-apart basin development based on Particle Flow Code (PFC) and simulation of deformation and earthquake potential of Ordos Block (China) under present tectonic stress regime based on Universal Distinct Element Code (UDEC). A scale-independent modeling approach based on PFC2D has been established to simulate the development of pull-apart basins. The micro-scale PFC models are used to investigate crack propagation and basin development in releasing sidestep systems with pure strike-slip, transtensional, and transpressional master faults, respectively. In each system, three typical models including 30° underlapping, 90° non-overlapping, and 150° overlapping releasing sidesteps are chosen. The modeling results are compared with pull-apart basins in nature. The geometric differences of pull-apart basins result from both the initial strike-slip fault geometries and its various evolution stages. Rhomboidal basins which have larger basin length than the amount of motion form in overlapping systems and do not progress through the spindle-shaped and lazy-Z-shaped stages such as the Dead Sea basin. Rhomboidal basins with cross-basin faults tend to form in underlapping systems. Finally, the origin of rhomboidal pull-apart basins, depocenters of pull-apart basins, cross-basin faults and their significances, models for pull-apart basin development, and minimum displacements and ages to form pull-apart basins are discussed. A two-dimensional UDEC model involving Ordos Block and adjacent areas is set up. Boundary conditions based on present tectonic regime are assumed. Block rotations, shear stress and displacement on faults, ratio of shear to normal force are simulated. Slip tendency which represents the assessment of the potential for causing slip on individual faults and earthquake-prone of the faults is predicted. Modeling results are compared with geologic evidences.

Ziel dieser Arbeit ist die Verbesserung der Vorhersagekraft des Bodenerosionsmodelierungs-werkzeugs EROSION-3D, welche oftmals durch die Identifizierung der werkzeugspezifischen Parameter Skinfaktor und Erosionswiderstand limitiert ist. Als drei Betrachtungsebenen der Arbeit werden 1. Beobachtungsdaten, 2. die Fähigkeit von EROSION-3D zur Beschreibung der Beobachtungsdaten und 3. die Vorhersagekraft des Werkzeugs untersucht. Aufzeichnungen verschiedener Beregnungsversuche wurden maschinenlesbar zusammengefasst. Daran wurde EROSION-3D mit den bisher üblichen sowie Monte-Carlo Methoden kalibriert. Anhand beschreibender Daten der Beregnungsversuche wurden Vorhersagemethoden zur Schätzung der modellspezifischen Parameter entwickelt und hinsichtlich der Parameterwerte und damit modellierter Abfluss-/Abtragswerte validiert. Die Ergebnisse zeigen, dass verbesserte Vorhersagen mit den neuen Schätzmethoden möglich sind, aber auch Möglichkeiten zur Verbesserung der Modellstruktur bestehen.

Reproducing the construction of a geoscientific model is a hard task. It requires the availability of all required data and an exact description how the construction was performed. In practice data availability and the exactness of the description is often lacking. As part of this thesis I introduce a conceptual framework how geoscientific model constructions can be described as directed acyclic hypergraphs, how such recorded construction graphs can be used to reconstruct the model, and how repetitive constructions can be used to verify the reproducibility of a geoscientific model construction process. In addition I present a software prototype, implementing these concepts. The prototype is tested with three different case studies, including a geophysical measurement analysis, a subsurface model construction and the calculation of a hydrological balance model.:1. Introduction 1.1. Survey on Reproducibility and Automation for Geoscientific Model Construction 1.2. Motivating Example 1.3. Previous Work 1.4. Problem Description 1.5. Structure of this Thesis 1.6. Results Accomplished by this Thesis 2. Terms, Definitions and Requirements 2.1. Terms and Definitions 2.1.1. Geoscientific model 2.1.2. Reproducibility 2.1.3. Realisation 2.2. Requirements 3. Related Work 3.1. Overview 3.2. Geoscientific Data Storage Systems 3.2.1. PostGIS and Similar Systems 3.2.2. Geoscience in Space and Time (GST) 3.3. Geoscientific Modelling Software 3.3.1. gOcad 3.3.2. GemPy 3.4. Experimentation Management Software 3.4.1. DataLad 3.4.2. Data Version Control (DVC) 3.5. Reproducible Software Builds 3.6. Summarised Releated Work 4. Concept 4.1. Construction Hypergraphs 4.1.1. Reproducibility Based on Construction Hypergraphs 4.1.2. Equality definitions 4.1.3. Design Constraints 4.2. Data Handling 5. Design 5.1. Application Structure 5.1.1. Choice of Application Architecture for GeoHub 5.2. Extension Mechanisms 5.2.1. Overview 5.2.2. A Shared Library Based Extension System 5.2.3. Inter-Process Communication Based Extension System 5.2.4. An Extension System Based on a Scripting Language 5.2.5. An Extension System Based on a WebAssembly Interface 5.2.6. Comparison 5.3. Data Storage 5.3.1. Overview 5.3.2. Stored Data 5.3.3. Potential Solutions 5.3.4. Model Versioning 5.3.5. Transactional security 6. Implementation 6.1. General Application Structure 6.2. Data Storage 6.2.1. Database 6.2.2. User-provided Data-processing Extensions 6.3. Operation Executor 6.3.1. Construction Step Descriptions 6.3.2. Construction Step Scheduling 6.3.3. Construction Step Execution 7. Case Studies 7.1. Overview 7.2. Geophysical Model of the BHMZ block 7.2.1. Provided Data and Initial Situation 7.2.2. Construction Process Description 7.2.3. Reproducibility 7.2.4. Identified Problems and Construction Process Improvements 7.2.5. Recommendations 7.3. Three-Dimensional Subsurface Model of the Kolhberg Region 7.3.1. Provided Data and Initial Situation 7.3.2. Construction Process Description 7.3.3. Reproducibility 7.3.4. Identified Problems and Construction Process Improvements 7.3.5. Recommendations 7.4. Hydrologic Balance Model of a Saxonian Stream 7.4.1. Provided Data and Initial Situation 7.4.2. Construction Process Description 7.4.3. Reproducibility 7.4.4. Identified Problems and Construction Process Improvements 7.4.5. Recommendations 7.5. Lessons Learned 8. Conclusions 8.1. Summary 8.2. Outlook 8.2.1. Parametric Model Construction Process 8.2.2. Pull and Push Nodes 8.2.3. Parallelize Single Construction Steps 8.2.4. Provable Model Construction Process Attestation References Appendix

Motivation dieser Arbeit ist die Weiterentwicklung des etablierten Prozesses der Sprühtrocknung, der Trocknung einer Flüssigkeit zu Partikeln mit definierter Form und Größe. Ist die zerstäubte Flüssigkeit eine reagierende Polymer- oder Monomerlösung wird der neuartige Prozess als Sprühpolymerisation bezeichnet. Da die Verweilzeiten in einem Sprühtrockner gering sind, wird die hochreaktive radikalische Kettenpolymerisation von Acrylsäure und Acrylaten im Lösungsmittel Wasser untersucht. Im Fokus der Arbeit ist die Methode der Rheokinetik. Diese Methode wertet die rheologische Veränderung der reagierenden Lösung aus, sodass in dieser Arbeit die Ergebnisse der Rheokinetik zur Prozessgestaltung diskutiert werden. Die Messungen zur Rheokinetik verschiedener Acrylatelösungen zeigen im Vergleich zur Acrylsäure geringere Viskositätsanstiege, die sich durch die geringe Reaktionsgeschwindigkeit in der pH-neutralen Lösung der Acrylate erklären lässt. Die Theorie zur Rheokinetik lässt sich nur auf die Acrylsäure anwenden, da diese überwiegend neutrale Polymerlösungen bildet und die Viskositätsfunktion über die Zeit mit einer Potenzfunktion beschrieben werden kann. Das Ergebnis ist ein empirisches Modell, was die Induktionszeit und den Viskositätsanstieg, der mit dem Umsatz der Reaktion korreliert, über die Zeit beschreibt. Die numerische Modellierung, die die Polymerisation und Trocknung des Einzeltropfens beschreibt, zeigt abschließend, dass eine Konditionierung des Trocknungsgases sowie eine Vorreaktion vor der Sprühpolymerisation anzustreben sind, damit der Prozess in einem konventionellen Sprühtrockner erfolgreich wird.:1 Einleitung 2 Stand der Technik 2.1 Sprühpolymerisationsverfahren 2.1.1 Trocknung am Einzeltropfen 2.2 Rheologische Eigenschaften von Flüssigkeiten im Viskosimeter und Rheometer 2.2.1 Messmethoden der Scherviskosität 2.3 Charakterisierung der Monomere 2.4 Polymerisation von Acrylsäure bzw. Acrylaten 2.4.1 Radikalische Lösungspolymerisation 2.4.2 Überblick über die Reaktionskinetik der radikalischen Polymerisation 2.4.3 Weitere Reaktionstypen bei der radikalischen Polymerisation 2.4.4 Einfluss des Lösungsmittels auf die radikalische Polymerisation 2.4.5 Einflüsse auf die Terminierung bei der radikalischen Polymerisation 2.4.6 Übersicht zur Messung der Kinetik bei Polymerisationen 2.4.7 Momentenmethode zur Berechnung der Polymerisation 2.5 Charakterisierung der Polymere 2.5.1 Polymere im Lösungsmittel 2.5.2 Skalierungstheorie nach de Gennes von Polymeren in Lösungsmitteln 2.5.3 Messmethoden der molaren Masse von Polymeren in Lösungsmitteln 2.5.4 Viskosität von Polymerlösungen 2.5.5 Intrinsische Viskosität von Polymerlösungen 2.6 Rheokinetik 3 Experimentelle Methoden 3.1 Material – Monomere und Polymere 3.1.1 Neutralisation von Acrylsäure zur Herstellung der Acrylate 3.1.2 Stoffwerte von Acrylsäure und Wassermischungen 3.1.3 Versuchsvorbereitung und Versuchsplan 3.2 Messmethodik der Rheokinetik 3.2.1 Versuchsdurchführung 3.2.2 Berücksichtigung der Verdunstung aus dem Probevolumen 3.2.3 Bestimmung von Umsatz und Polymerisationsgrad 4 Ergebnisse zur Rheokinetik 4.1 Rheokinetik am wässrigen System mit Acrylsäure bzw. Acrylaten 4.1.1 Erläuterung zur Auswertungsprozedur an verschiedenen Rohdaten von Acrylsäure und Acrylaten 4.1.2 Ergebnisdiskussion zur Rheokinetik bei wässrigen Acrylsäure- bzw. Acrylatlösungen 4.2 Rheokinetik mit Modellbildung zur Polymerisation wässriger Acrylsäure Lösungen 4.2.1 Empirisches Modell zur Funktion η(t) 4.2.2 Modellierung der Rheokinetik 4.2.3 Bewertung der Rheokinetik durch Messungen von Umsatz und Viskosität im Rheometer 5 Numerische Modellierung von Reaktion und Trocknung 5.1 Numerische Modellierung der Reaktion im Rheometer 5.1.1 Ergebnisse der Momentenmethode für die Reaktion im Rheometer 5.2 Numerische Modellierung zur Reaktion im Sprühtrockner 5.2.1 Ergebnisse der Modellierung am Tropfen 6 Zusammenfassung und Ausblick 6.1 Ergebnisse zur Rheokinetik 6.2 Numerische Modellierung 6.3 Ausblick

This thesis documents the development of a simulation strategy to model the behavior of geomembranes at large deformations using the explicit finite difference code FLAC3D. The geomembrane is represented by special shell elements and interfaces at both sides of the geomembrane duplicating the interaction with the overlying and underlying materials. Chapter 1 provides an introduction to geotextiles and geomembranes, and their use in geotechnical engineering. Special attention is paid to pull-out tests because of their importance to describe the behavior at large deformations. Chapter 2 describes the proposed ‘liner’ model concept to simulate the interaction of a geomembrane with the over- and underlying material. Furthermore, this chapter documents in detail the simulation of uniaxial pull-out tests for validation of the proposed ‘liner’ model concept and compares it with the FLAC3D built-in geogrid element. To clarify more clearly the potential failure (crack propagation and rupture process) of the geomembrane, the ‘liner’ model under biaxial loading was investigated in Chapter 3. Chapter 4 documents a detailed parameter study with a special focus on the stiffness and frictional behavior of the ‘liner’ element using a simplified waste dump. In chapter 5 a new constitutive model (“Femesalz”) is proposed to describe the visco-elasto-plastic behavior of crushed salt and waste rock salt, respectively. The “Femesalz” constitutive model together with the ‘liner’ model is applied to simulate the behavior of a rock salt waste dump (2.5-dimensional) to validate both, the new constitutive model “Femesalz” as well as the ‘liner’ model. Chapter 6 documents the use of the ‘liner’ element and the “Femesalz” constitutive model to simulate salt dump models in 2D and 3D on different terrain types (mountain, valley, plain) for a time of 100 years to generate large deformations. Chapter 7 contains the main conclusions and recommendations.:ABSTRACT AND STRUCTURE OF THESIS 2 ACKNOWLEDGMENTS 4 CONTENTS 5 LIST OF TABLES 7 LIST OF FIGURES 10 NOMENCLATURE 16 CHAPTER 1: INTRODUCTION AND STATE-OF-THE-ART 22 1.1 Geosynthetic for geoengineering projects (overview) 22 1.2 Pull-out tests (overview) 29 CHAPTER 2: “LINER” CONCEPT AND NUMERICAL SIMULATIONS OF UNIAXIAL PULL-OUT TESTS 39 2.1 Introduction 39 2.2 Numerical calculations 39 2.2.1 General considerations 39 2.2.2 Concept of the 'liner' element 40 2.2.3 'Geogrid' versus 'liner' element 41 2.2.4 Verification of ‘liner’ element 42 2.2.5 Conclusions 58 CHAPTER 3: BIAXIAL LOADING OF “LINER” MODEL 61 3.1 Introduction 61 3.2 Model set-up 61 3.3 Results of biaxial pull-out test simulation 63 3.4 Summary and Conclusions 71 CHAPTER 4: PARAMETER STUDY OF EMBEDDED GEOMEMBRANE 74 4.1 Introduction 74 4.2 Model set-up 74 4.3 Results 77 4.3.1 Influence of interface stiffness 80 4.3.2 Influence of interface friction 87 4.4 Conclusions 93 CHAPTER 5: CONSTITUTIVE MODEL FOR SALT DUMP 95 5.1 Introduction 95 5.1.1 Overview of constitutive models for rock salt 97 5.1.2 Overview of constitutive models for crushed salt 104 5.2 ‘Femesalz’ constitutive model for crushed salt 106 5.2.1 Introduction 106 5.2.2 Compaction test 111 5.2.3 Triaxial test and realistic waste dump simulation 114 5.2.4 Numerical salt dump simulations 115 5.3 Summary 122 CHAPTER 6: SIMULATIONS CONSIDERING TOPOGRAPHY OF UNDERLYING MATERIAL 123 6.1 Introduction 123 6.2 Model set-up 123 6.3 Model parameters and calculation sequence 131 6.4 Calculation results 132 6.5 Discussion of results and conclusions 139 CHAPTER 7: CONCLUSIONS 141 REFERENCE 143

Um das Verständnis für physikalische und biologische Dynamiken zu verbessern, werden oft stellvertretend mathematische Modelle entwickelt, implementiert,validiert und analysiert. Die Entscheidung für oder gegen einen bestimmten Modelltyp, zum Beispiel ob die Auflösung in Raum und Zeit diskret oder kontinuierlich definiert ist, kann erheblichen Einfluss auf die Ergebnisse haben. Insbesondere bei der Untersuchung und Simulation der Dynamiken von biologischen Zellen, die häufig auch als biologische Flüssigkeiten (Biofluids) bezeichnet und in der Literatur oft mit physikalischen Flüssigkeiten verglichen werden, ist die Wahl des geeigneten Modelltyps nicht immer trivial. In diesem Zusammenhang stellt die vorliegende Arbeit drei verschiedene Szenarien vor. Unter Zuhilfenahme von unterschiedlichen mathematischen Modellen werden diese Szenarien dann untersucht. Dabei wird deutlich, dass trotz des ähnlichen Kontextes von physikalischen und biologischen Dynamiken je Szenario unterschiedliche Modelltypen besser geeignet sind und mitunter verschiedene Aussagen liefern. Daher muss für jedes dieser Szenarien die Entscheidung, welches Modell genommen wird und ob dieses in Raum und Zeit diskret oder kontinuierlich ist, neu evaluiert werden. Das erste Szenario befasst sich mit einer rein physikalischen Dynamik und beschreibt das Aufsteigen einer runden Flüssigkeitsblase innerhalb einer anderen Flüssigkeit. In diesem Zusammenhang wird auch häufig von zwei Phasen gesprochen. Dieser Fall dient auch als numerischer Benchmark-Test zur Bewertung der Genauigkeit von Zwei-Phasen-Modellen. Innerhalb dieses Kontextes werden oft Modelle verwendet, die kontinuierlich in Bezug auf Ort und Zeit sind. In der vorliegenden Arbeit wird stellvertretend das Cahn-Hilliard-Navier-Stokes-Modell verwendet. Vor allem wird ein neuer einfacher Diskretisierungsansatz für dieses Modell vorgestellt. Unter Verwendung eines Standard-Benchmark-Tests wird gezeigt, dass die Genauigkeit vergleichbar zu bisherigen Methoden ist. Das zweite Szenario fokussiert sich auf eine biologische Dynamik und beschreibt das Wachstum eines Tumorsphäroiden und sein Verhalten bei der Behandlung mit Radiostrahlung. Tumorsphäroide sind spezielle 3D in-vitro Experimente, welche eine Ansammlung von mehreren tausend Zellen umfassen und Tumormikroumgebung und Mikrometastasen nachempfinden. Durch ihre 3D Struktur zeigen sie Stoffwechselgradienten von Sauerstoff, Nährstoffen und Abfallprodukten. Die Modellierung solcher Sphäroide wird häufig mit zell- oder agentenbasierten Modellen beschrieben, die in Bezug auf Ort und Zeit meist diskret sind und das Zellverhalten regelbasiert beschreiben. In dieser Arbeit wird hierfür stellvertretend ein zellulärer Automat verwendet. Dieser dient später als Vergleichsmodell zu dem neu entwickelten und hier vorgestellten Ansatz: dem 1D Radial Shell Modell, welches im Ort diskret und in der Zeit kontinuierlich ist. Dieses ermöglicht weitere Erkenntnisse und Vorhersagen zum Wachstum der Sphäroide, insbesondere für die Dynamik bei kleinem Sphäroidvolumen. Im dritten Szenario wird ein Grenzfall zwischen den physikalischen und biologischen Flüssigkeiten beschrieben: Die Entmischungsdynamik von biologischen Zellen, welche oft in der Literatur mit der Entmischung von zwei physikalischen Flüssigkeiten, wie Wasser und Öl, verglichen wird. Daher werden die beiden zuvor vorgestellten Modelle, das kontinuierliche Cahn-Hilliard-Navier-Stokes-Modell und der diskrete zelluläre Automat, für diesen Sachverhalt simuliert und analysiert. Zudem werden beide Modelle miteinander und jeweils mit biologischen Experimenten verglichen, wobei aufgrund ihrer unterschiedlichen zeitlichen und räumlichen Auflösung verschiedene Vor- und Nachteile identifizierbar sind. Am Ende zeigt sich entgegen bisherigen Versuchen in der Literatur, dass die Anpassung der Modelle an die Experimentaldaten nicht ausschließlich durch das Skalierungsverhalten machbar ist, da die Zeitskalen in den Experimenten häufig zu kurz sind. Daher sollten zusätzliche Metriken, wie zum Beispiel der durchschnittliche Clusterdurchmesser oder die Verteilung der Clustergrößen, beachtet werden. / Enhancing the understanding of physical and biological dynamics is crucial, which is why assisting mathematical models are often developed, implemented, validated, and analyzed. The decision for or against a particular model type, for example, whether the resolution in space and time is defined discretely or continuously, can considerably influence the results. Especially when investigating and simulating the dynamics of biological cells, also referred to as biological fluids and in the literature often compared to physical fluids, choosing the appropriate model type is not trivial in every case. This work presents three scenarios, which are further examined with the help of various mathematical models. Despite the similar context, dynamics of physical and biological fluids, some model types are more suited and deliver different results for each scenario. Therefore, the decision should be made new, depending on the scenarios, which model type is optimal, discrete, or continuous in space and time. The first scenario describes pure physical dynamics by the rise of a round fluid bubble within another fluid, which is often referred to as two phases. This setup also serves as a numerical benchmark test to evaluate the accuracy of physical two-phase-models. Within this context, the models used are often continuous regarding space and time. In this work, the Cahn-Hilliard-Navier-Stokes-model is chosen as a representative example. In particular, a new discretization approach for the model is introduced and evaluated by the previous benchmark test, which showcases that the new, more straightforward discretization approach leads to comparably precise results. The second scenario focuses on biological dynamics and describes the untreated growth of a tumor spheroid and further its behavior when exposed to \acl{rt}. These tumor spheroids are, in particular, 3D-assays of in-vitro experiments, which are 3D avascular aggregates of several thousand tumor cells mimicking tumor microareas or micrometastases. Due to their 3D structure, spheroids exhibit metabolic gradients of oxygen, nutrients, and waste products. These are usually simulated with cell or agent-based models, which are discrete in terms of space and time and describe the cell behavior in a rule-based manner. In this work, a cellular automaton is used as a representative. Later, this model will serve as a comparison for the new innovative approach presented here: the 1D Radial Shell model, which is space-discrete and time-continuous. This model allows further insights and predictions, for example, regarding the behavior of spheroids at small volumes, justifying the use of multiple model types. The third scenario can be seen as the in-between of physical and biological fluid dynamics: The segregation of biological cells of two distinct types, which is in the literature often referred to as similar or equal to that of two physical fluids, like oil and water. Therefore, this process is simulated and analyzed with the previously introduced continuous Cahn-Hilliard-Navier-Stokes and the discrete cellular automaton models. Thereby, both models are compared with each other and also individually with biological experiments. The comparison enables the identification of various advantages and disadvantages due to their different temporal and spatial resolution. In the end, it becomes clear that adapting the models to the experimental data is only partially feasible through the scaling behavior, as the time scale in the experiments is often too short, which stands in contrast to the current standard in the literature. Therefore, we emphasize that additional metrics should be considered, such as the average cluster diameter or cluster size distribution.