Journal of Computational Physics

Fluid-solid interaction (FSI) phenomena play an important role in many biomedical engineering applications. While FSI techniques and models have enabled detailed computational simulations of flow and tissue motion, the application of FSI can ...

• Novel model reduction for cardiovascular fluid-solid interaction (FSI).
• Physics- and projection-based approach to address the solid mechanics problem in FSI.
• Suitable for modeling large-deformation mechanics using ‘fluid-only’ ...

The extended Fisher–Kolmogorov (EFK) equation has been used to describe some phenomena in physical, material and biological systems. In this paper, we propose a full-rank splitting scheme and a rank-adaptive splitting approach for this equation. ...

• The EFK equation is split into three subproblems, then a full-rank splitting scheme is established. The convergence of this scheme is analyzed.
• A rank-adaptive low-rank approach is proposed for the EFK equation. To the best of our ...

We introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial differential ...

• Novel AMR paradigm based on anticipating future simulation errors.
• Leverages recent advancements in multi-agent reinforcement learning.
• Significant efficiency improvements over traditional AMR techniques.
• Applications to ...

We present and analyze a series of benchmark tests regarding the application of the immersed boundary (IB) method to viscoelastic flows through and around non-trivial, stationary geometries. The IB method is widely used to simulate biological ...

• The Immersed Boundary method is applied to viscoelastic flows around non-trivial, stationary geometries.
• Computational results are compared to previous numerical benchmarks and macrorheology experiments.
• Choices of relative ...

The Immersed Boundary (IB) method of Peskin (1977) [1] is useful for problems that involve fluid-structure interactions or complex geometries. By making use of a regular Cartesian grid that is independent of the geometry, the IB framework yields ...

• Reformulated Immersed Boundary method for double layer integral equations.
• Efficient IB constraint method for PDEs with prescribed boundary values.
• Well-conditioned IB method resulting from second-kind integral equation ...

• The conventional multi-phase WCSPH and EISPH are improved through reformulation as a quasi-Lagrangian scheme based on ALE formulation.
• Two explicit multi-phase SPH methods are coupled to EICSPH for simulating multiphase flows where ...

This study presents three Smoothed Particle Hydrodynamics (SPH) methods capable of handling high-density differences in violent incompressible multiphase flows. The conventional Weakly Compressible SPH (WCSPH) is reformulated into a quasi-...

In this paper, we propose a generalized Riemann problem (GRP) scheme for a laminar two-phase flow model. The model takes into account the distinctions between different densities and velocities, and is obtained by averaging vertical velocities ...

This paper presents high-order finite volume multi-resolution weighted essentially non-oscillatory schemes with adaptive linear weights to solve hyperbolic conservation laws on triangular meshes. They are abbreviated as the ALW-MR-WENO schemes. ...

• We design high-order finite volume multi-resolution weighted essentially non-oscillatory schemes with adaptive linear weights on triangular meshes. They use only two unequal-sized central spatial stencils to obtain arbitrarily high-order ...

The direct simulation Monte Carlo (DSMC) method is widely used for numerical solutions of the Boltzmann equation. However, the associated computational cost becomes prohibitive in the near-continuum regime. To address this limitation, the ...

• A new diatomic kinetic model based on the Fokker–Planck and equations.
• The correct Prandtl number, accurate relaxation rates for internal energies, and the H-theorem are included in the model.
• The development of a conservative ...

The work discusses a new low-rank Monte Carlo technique to solve Smoluchowski-like kinetic equations. It drastically decreases the computational complexity of modeling of size-polydisperse systems. For the studied systems it can outperform the ...

• Low-rank approximation accelerates Monte Carlo simulations.
• Segment trees are used to quickly select particle pairs.
• Applicable to classical and temperature-dependent Smoluchowski equations.

Dynamic mode decomposition (DMD) describes the dynamical system in an equation-free manner and can be used for the prediction and control. It is an efficient data-driven method for the complex systems. In this paper, we extend DMD to the ...

• The presented novel upwind moving least squares approximation can satisfy positive operator condition.
• Suggested upwind method can successfully overcome the problem of nonphysical oscillation encountering convection-dominated partial ...

Moving Least Squares (MLS), as a series representation type of approximation, is broadly used in a wide array of meshfree methods. However, using the existing standard form of the MLS causes an unphysical oscillation for the meshfree methods ...

Compressible flows typically exhibit multiple shock waves which interact with each other, making the detection of these shock waves crucial for various aspects of flow studies including construction of high-order numerical schemes (e.g., shock-...

In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive ...

In this work we propose and investigate the performance of a metric-based refinement criteria for adaptive meshing used for improving the numerical solution of an elliptic problem. We show that in general, when solving elliptic equations such as ...

• Extension of Riemannian metric-based theory to square/cubic elements.
• Measure of the performance of local interpolation methods for elliptic equations.
• Identification of a new error source attributed to the local element size ...

In this paper, we introduce a hybrid LBM-FVM solver for two-phase fluid flow simulations in which interface dynamics is modeled by a conservative phase-field equation. Integrating fluid equations over time is achieved through a velocity-based ...

• This paper proposes a new hybrid LBM-FVM solver to simulate two-phase flows which reduces memory consumption and improves computational accuracy and efficiency.
• The momentum equation is solved by a set of lattice Boltzmann equations ...

This study presents a collection of purely data-driven workflows for constructing reduced-order models (ROMs) for distributed dynamical systems. The ROMs we focus on, are data-assisted models inspired by, and templated upon, the theory of ...

• Machine learning motivates revisiting post-processing Galerkin ROMs.
• Diffusion Maps & autoencoders discover relations between sets of latent variables.
• Data-driven workflows produce ROM closures to enhance accuracy.
• “Gray box” ...

In this paper, we propose a type of tensor-neural-network-based machine learning method to compute multi-eigenpairs of high dimensional eigenvalue problems without Monte-Carlo procedure. Solving multi-eigenvalues and their corresponding ...

Triangular surface-based 3D IIM (Immersed Interface Method) algorithms face major challenges due to the need to calculate surface derivative of jumps. This paper proposes a fast, easy-to-implement, surface-derivative-free of jumps, augmented IIM (...

• A novel, easy-to-implement and fast augmented simplified IIM is proposed for 3D Helmholtz interface problems.
• It seems to be the first work on IIM with the triangular surface mesh indeed.
• The method provides a fairly simple way to ...

Developing surrogate models for costly mathematical models representing physical systems is challenging since it is typically not possible to generate large training data sets, i.e. to create a large experimental design. In such cases, it can be ...

• PC2 – a novel framework for physically constrained polynomial chaos expansions is proposed.
• An efficient algorithm based on constrained least squares and sparse solver is developed.
• Analytical uncertainty quantification of ...

We introduce an efficient numerical implementation of a Markov Chain Monte Carlo method to sample a probability distribution on a manifold (introduced theoretically in Zappa, Holmes-Cerfon, Goodman (2018) [53]), where the manifold is defined by ...

• Introduces numerical algorithm for sampling probability distribution on a manifold.
• Manifold is defined by level set of constraint functions, such as bond-distances.
• Algorithm is efficient in problems with thousands of dimensions.

Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs). In this work, we focus on multiscale PDEs that have important ...

In this study, we conduct a parametric analysis to evaluate the sensitivities of wall-modeled large-eddy simulation (LES) with respect to subgrid-scale (SGS) models, mesh resolution, wall boundary conditions and mesh anisotropy. While such ...

• This study is among the first to explore the sensitivities of wall-modeled LES for separated turbulent flow.
• Subgrid-scale model exerts a significant influence on the wall-modeled LES for separated turbulent flow.
• The impact of the ...

Bayesian update is a common strategy used to combine (uncertain) model predictions and (noisy) observational data. A computational bottleneck in this data assimilation technique is the evaluation of high-dimensional quadratures involving ...

• The use of “designed quadratures” (DQ) reduces the computational cost of Bayesian update of multivariate joint distributions.
• The DQ error decays with the number of quadrature nodes faster than the errors of either Monte Carlo or ...

A data-driven model is compared to classical equation-driven approaches to investigate its ability to predict quantity of interest and their uncertainty when studying airfoil aerodynamics. The focus is on autoencoders and the effect of ...

• Proposed autoencoder ensemble distinguishes between different sources of uncertainty.
• The approach correctly identifies regions of low prediction confidence.
• The standard deviation of the ensemble is a reasonable proxy for the ...

We introduce Weak-PDE-LEARN, a Partial Differential Equation (PDE) discovery algorithm that can identify non-linear PDEs from noisy, limited measurements of their solutions. Weak-PDE-LEARN uses an adaptive loss function based on weak forms to ...

• We introduce weak-PDE-LEARN, a novel approach to learning a hidden PDE by leveraging its weak form.
• Weak-PDE-LEARN trains a deep neural network to learn an approximation to one of the hidden PDE's solutions.
• Our approach uses a ...

Data assimilation is crucial in a wide range of applications, but it often faces challenges such as high computational costs due to data dimensionality and incomplete understanding of underlying mechanisms. To address these challenges, this study ...

• Implicit neural representations help establish a mesh-free assimilation framework.
• Spherical harmonics bring theoretical guarantee for the neural network.
• Uncertainty of trained model is evaluated; compatible with existing ...

Multi-fidelity strategies leverage a large amount of low-fidelity data combined with a smaller set of high-fidelity data, thereby achieving satisfactory results at a reasonable cost. In our research, we introduce an innovative multi-fidelity ...

• Analyze and compare mainstream methods of multi-fidelity surrogate model.
• A novel multi-fidelity surrogate model.
• Achieve higher accuracy and stability with a small number of high-fidelity samples.
• A general method that can ...

• Not applicable. This is not a research paper but one on the history of CFD.

The genesis and contents of the 2010 poster "History of CFD Part II" are described.