Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows

Unilateral external fixator and its biomechanical effects in treating different types of femoral fracture: A finite element study with experimental validated model

Previous works had successfully demonstrated the clinical effectiveness of unilateral external fixator in treating various types of fracture, ranging from the simple type, such as oblique and transverse fractures, to complex fractures. However, literature that investigated its biomechanical analyses to further justify its efficacy is limited. Therefore, this paper aimed to analyse the stability of unilateral external fixator for treating different types of fracture, including the simple oblique, AO32C3 comminuted, and 20 mm gap transverse fracture. These fractures were reconstructed at the distal diaphysis of the femoral bone and computationally analysed through the finite element method under the stance phase condition. Findings showed a decrease in the fixation stiffness in large gap fracture (645.2 Nmm-1 for oblique and comminuted, while 23.4 Nmm-1 for the gap fracture), which resulted in higher displacement, IFM and stress distribution at the pin bone interface. These unfavourable conditions could consequently increase the risk of delayed union, pin loosening and infection, as well as implant failure. Nevertheless, the stress observed on the fracture surfaces was relatively low and in controlled amount, indicating that bone unity is still allowable in all models. Briefly, the unilateral fixation may provide desirable results in smaller fracture gap, but its usage in larger gap fracture might be alarming. These findings could serve as a guide and insight for surgeons and researchers, especially on the biomechanical stability of fixation in different fracture types and how will it affect bone unity.

Efficient Iterative Arbitrary High-Order Methods: an Adaptive Bridge Between Low and High Order

We propose a new paradigm for designing efficient p-adaptive arbitrary high-order methods. We consider arbitrary high-order iterative schemes that gain one order of accuracy at each iteration and we modify them to match the accuracy achieved in a specific iteration with the discretization accuracy of the same iteration. Apart from the computational advantage, the newly modified methods allow to naturally perform the p-adaptivity, stopping the iterations when appropriate conditions are met. Moreover, the modification is very easy to be included in an existing implementation of an arbitrary high-order iterative scheme and it does not ruin the possibility of parallelization, if this was achievable by the original method. An application to the Arbitrary DERivative (ADER) method for hyperbolic Partial Differential Equations (PDEs) is presented here. We explain how such a framework can be interpreted as an arbitrary high-order iterative scheme, by recasting it as a Deferred Correction (DeC) method, and how to easily modify it to obtain a more efficient formulation, in which a local a posteriori limiter can be naturally integrated leading to the p-adaptivity and structure-preserving properties. Finally, the novel approach is extensively tested against classical benchmarks for compressible gas dynamics to show the robustness and the computational efficiency.

Stress State in an Eccentric Elastic Ring Loaded Symmetrically by Concentrated Forces

The stress state from an eccentric ring made of an elastic material symmetrically loaded on the outer boundary by concentrated forces is deduced. The analytical results are obtained using the Airy stress function expressed in bipolar coordinates. The elastic potential corresponding to the same loading but for a compact disk is first written in bipolar coordinates, then expanded in Fourier series, and after that, an auxiliary potential of a convenient form is added to it in order to impose boundary conditions. Since the inner boundary is unloaded, boundary conditions may be applied directly to the total potential. A special focus is on the number of terms from Fourier expansion of the potential in bipolar coordinates corresponding to the compact disk as this number influences the sudden increase if the coefficients from the final form of the total potential. Theoretical results are validated both by using finite element software and experimentally through the photoelastic method, for which a device for sample loading was designed and constructed. Isochromatic fields were considered for the photoelastic method. Six loading cases for two different geometries of the ring were studied. For all the analysed cases, an excellent agreement between the analytical, numerical and experimental results was achieved. Finally, for all the situations considered, the stress concentration effect of the inner hole was analytically determined. It should be mentioned that as the eccentricity of the inner hole decreases, the integrals from the relations of the total elastic potential present a diminishing convergence in the vicinity of the inner boundary.

An Unconditional Positivity-Preserving Difference Scheme for Models of Cancer Migration and Invasion

In this paper, we consider models of cancer migration and invasion, which consist of two nonlinear parabolic equations (one of the convection–diffusion reaction type and the other of the diffusion–reaction type) and an additional nonlinear ordinary differential equation. The unknowns represent concentrations or densities that cannot be negative. Widely used approximations, such as difference schemes, can produce negative solutions because of truncation errors and can become unstable. We propose a new difference scheme that guarantees the positivity of the numerical solution for arbitrary mesh step sizes. It has explicit and fast performance even for nonlinear reaction terms that consist of sums of positive and negative functions. The numerical examples illustrate the simplicity and efficiency of the method. A numerical simulation of a model of cancer migration is also discussed.