Per-Olof Persson

• University of California, Berkeley

We present a geometric multigrid solver based on adaptive smoothed aggregation suitable for Discontinuous Galerkin (DG) discretisations. Mesh hierarchies are formed via domain decomposition techniques, and the method is applicable to fully unstructured meshes using arbitrary element shapes. Furthermore, the method can be employed for a wide range o...

In this work we introduce a triangular Delaunay mesh generator that can be trained using reinforcement learning to maximize a given mesh quality metric. Our mesh generator consists of a graph neural network that distributes and modifies vertices, and a standard Delaunay algorithm to triangulate the vertices. We explore various design choices and ev...

We present a new decomposition of a Cauchy–Vandermonde matrix as a product of bidiagonal matrices which, unlike its existing bidiagonal decompositions, is now valid for a matrix of any rank. The new decompositions are insusceptible to the phenomenon known as subtractive cancellation in floating point arithmetic and are thus computable to high relat...

The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations, where differentiable programming plays a crucial role in calculating model sensitivities, inverting model parame...

We introduce the concept of half-closed nodes for nodal Discontinuous Galerkin (DG) discretisations. This is in contrast to more commonly used closed nodes in DG where in each element nodes are placed on every boundary. Half-closed nodes relax this constraint by only requiring nodes on a subset of the boundaries in each element, with this extra fre...

Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post‐processing step in mesh generation procedures and in applications such as fluid simulations with severely deforming domains. In o...

WIND turbine blade monitoring for damage offers significant benefits in terms of both economic savings and sustainability [1–5]. It is critical to identify and repair damage as soon as possible to limit turbine downtime, minimize repair costs, and prevent catastrophic component failure. An acoustics-based approach proposed by Niezrecki and Inalpola...

Mesh optimization procedures are generally a combination of node smoothing and discrete operations which affect a small number of elements to improve the quality of the overall mesh. These procedures are useful as a post-processing step in mesh generation procedures and in applications such as fluid simulations with severely deforming domains. In o...

We present a new high-order accurate discretisation on unstructured meshes of quadrilateral elements. Our Face Upwinded Spectral Element (FUSE) method uses the same node distribution as a high-order continuous Galerkin (CG) method, but with a particular choice of node locations within each element and an upwinded stencil on the face nodes. This res...

We present a class of preconditioners for the linear systems resulting from a finite element or discontinuous Galerkin discretizations of advection-dominated problems. These preconditioners are designed to treat the case of geometrically localized stiffness, where the convergence rates of iterative methods are degraded in a localized subregion of t...

We present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (q-, h-) Bernstein-Vandermonde ones, among others. These results generalize the existing expressions for nonsingular matrices to matrices of arbitrary rank. For totally nonnegative matrices of the above classes, the n...

We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which when differentiated provides the derivatives of the original function. The method generalises traditional finite...

A recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws [43], [45] is extended to the unsteady case. Central to the framework is an optimization problem which simultaneously computes a discontinuity-aligned mesh and the corresponding high-order approximati...

We present a framework for resolving discontinuous solutions of conservation laws using implicit tracking and a high-order discontinuous Galerkin (DG) discretization. Central to the framework is an optimization problem and associated sequential quadratic programming solver which simultaneously solves for a discontinuity-aligned mesh and the corresp...

This article considers a new discretization scheme for conservation laws. The discretization setting is based on a discontinuous Galerkin scheme in combination with an approximation space that contains high-order polynomial modes as well as piece-wise constant modes on a sub-grid. The high-order modes can continuously be suppressed with a penalty f...

We present a geometric multigrid solver for the Compact Discontinuous Galerkin method through building a hierarchy of coarser meshes using a simple agglomeration method which handles arbitrary element shapes and dimensions. The method is easily extendable to other discontinuous Galerkin discretizations, including the Local DG method and the Interio...

View Video Presentation: https://doi.org/10.2514/6.2021-2614.vid This paper presents a fluid-structure interaction parameter space study focused on the development of leading edge vortices (LEVs) on two-dimensional, bio-inspired wings. The unsteady aerodynamics are computationally modeled using a linear-strength doublet lattice panel method incorpo...

We present a novel approach for high-order accurate numerical differentiation on unstructured meshes of quadrilateral elements. To differentiate a given function, an auxiliary function with greater smoothness properties is defined which when differentiated provides the derivatives of the original function. The method generalises traditional finite...

A recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws [41, 43] is extended to the unsteady case. Central to the framework is an optimization problem which simultaneously computes a discontinuity-aligned mesh and the corresponding high-order approximation...

A mesh motion test case has been part of the High-Fidelity (previously High-Order) CFD Workshop since its inception in 2012. The number of groups participating has been small, and most submissions have used an Arbitrary Lagrangian Eulerian formulation, although this is not required. The initial cases involved the interaction of moving airfoils and...

This chapter introduces some of the most popular implicit time-integration methods, and a highly efficient preconditionerPreconditioner, preconditioning based on block-ILUIncomplete factorization, incomplete LU factorization, ILU factorizations and Minimum Discarded Fill element ordering. It also describes how to combine the benefits of both explic...

The book introduces modern high-order methods for computational fluid dynamics. As compared to low order finite volumes predominant in today's production codes, higher order discretizations significantly reduce dispersion errors, the main source of error in long-time simulations of flow at higher Reynolds numbers. A major goal of this book is to te...

We present a geometric multigrid solver for the Compact Discontinuous Galerkin method through building a hierarchy of coarser meshes using a simple agglomeration method which handles arbitrary element shapes and dimensions. The method is easily extendable to other discontinuous Galerkin discretizations, including the Local DG method and the Interio...

Purpose Three‐dimensional, time‐resolved blood flow measurement (4D‐flow) is a powerful research and clinical tool, but improved resolution and scan times are needed. Therefore, this study aims to (1) present a postprocessing framework for optimization‐driven simulation‐based flow imaging, called 4D‐flow High‐resolution Imaging with a priori Knowle...

We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1], [2], which used implicit-explicit Runge-Kutta methods (IMEX) to build high-order, partitioned multiphysics s...

A novel framework for resolving discontinuous solutions of conservation laws, e.g., contact lines, shock waves, and interfaces, using implicit tracking and a high-order discontinuous Galerkin (DG) discretization was introduced in [39]. Central to the framework is an optimization problem whose solution is a discontinuity-aligned mesh and the corresp...

A novel framework for resolving discontinuous solutions of conservation laws, e.g., contact lines, shock waves, and interfaces, using implicit tracking and a high-order discontinuous Galerkin (DG) discretization was introduced in [38]. Central to the framework is an optimization problem whose solution is a discontinuity-aligned mesh and the corresp...

This article considers a new discretization scheme for conservation laws. The discretization setting is based on a discontinuous Galerkin scheme in combination with an approximation space that contains high-order polynomial modes as well as piece-wise constant modes on a sub-grid. The high-order modes can continuously be suppressed with a penalty f...

This article considers a new discretization scheme for conservation laws. The discretization setting is based on a discontinuous Galerkin scheme in combination with an approximation space that contains high-order polynomial modes as well as piece-wise constant modes on a sub-grid. The high-order modes can continuously be suppressed with a penalty f...

We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1, 2], which used implicit-explicit Runge-Kutta methods (IMEX) to build high-order, partitioned multiphysics sol...

We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions, this method guarantees that the discrete integral of the entropy is non-increasing. This nonlinear entropy stabil...

A high-order accurate adjoint-based optimization framework is presented for unsteady multiphysics problems. The fully discrete adjoint solver relies on the high-order, linearly stable, partitioned solver introduced in [1], where different subsystems are modeled and discretized separately. The coupled system of semi-discretized ordinary differential...

The problem of solution transfer between meshes arises frequently in computational physics, e.g. in Lagrangian methods where remeshing occurs. The interpolation process must be conservative, i.e. it must conserve physical properties, such as mass. We extend previous works --- which described the solution transfer process for straight sided unstruct...

We develop a discretely entropy-stable line-based discontinuous Galerkin method for hyperbolic conservation laws based on a flux differencing technique. By using standard entropy-stable and entropy-conservative numerical flux functions, this method guarantees that the discrete integral of the entropy is non-increasing. This nonlinear entropy stabil...

This work introduces a general framework for constructing high-order, linearly stable, partitioned solvers for multiphysics problems from a monolithic implicit-explicit Runge-Kutta (IMEX-RK) discretization of the semi-discrete equations. The generic multiphysics problem is modeled as a system of n systems of partial differential equations where the...

This work introduces a general framework for constructing high-order, linearly stable, partitioned solvers for multiphysics problems from a monolithic implicit-explicit Runge-Kutta (IMEX-RK) discretization of the semi-discrete equations. The generic multiphysics problem is modeled as a system of n systems of partial differential equations where the...

We study the convergence of iterative linear solvers for discontinuous Galerkin discretizations of systems of hyperbolic conservation laws with polygonal mesh elements compared with that of traditional triangular elements. We solve the semi-discrete system of equations by means of an implicit time discretization method, using iterative solvers such...

We study the convergence of iterative linear solvers for discontinuous Galerkin discretizations of systems of hyperbolic conservation laws with polygonal mesh elements compared with that of traditional triangular elements. We solve the semi-discrete system of equations by means of an implicit time discretization method, using iterative solvers such...

A globally high-order numerical discretization of time-dependent conservation laws on deforming domains, and the corresponding fully discrete adjoint method, is reviewed and applied to determine energetically optimal flapping wing motions subject to aerodynamic constraints using a reduced space PDE-constrained optimization framework. The conservati...

This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous Galerkin methods. The proposed method aims to align inter-element boundaries with discontinuities in the solutio...

This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous Galerkin methods. The proposed method aims to align inter-element boundaries with discontinuities in the solutio...

In this paper, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to approximate the exact block Jacobi preconditioner by Kronecker products of several small, one-dimensional matrices. Tra...

In this paper, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to approximate the exact block Jacobi preconditioner by Kronecker products of several small, one-dimensional matrices. Tra...

In this paper, we develop new techniques for solving the large, coupled linear systems that arise from fully implicit Runge-Kutta methods. This method makes use of the iterative preconditioned GMRES algorithm for solving the linear systems, which has seen success for fluid flow problems and discontinuous Galerkin discretizations. By transforming th...

In this paper, we develop new techniques for solving the large, coupled linear systems that arise from fully implicit Runge-Kutta methods. This method makes use of the iterative preconditioned GMRES algorithm for solving the linear systems, which has seen success for fluid flow problems and discontinuous Galerkin discretizations. By transforming th...

Stromboli is a model volcano for studying eruptions driven by degassing. The current paradigm posits that Strombolian eruptions represent the bursting of gas slugs ascending through melt-filled conduits, but petrological observations show that magma at shallow depth is crystalline enough to form a three-phase plug consisting of crystals, bubbles an...

The fully discrete adjoint method, corresponding to a globally high-order accurate dis-cretization of the compressible Navier-Stokes equations on deforming domains, is introduced. A mapping-based Arbitrary Lagrangian-Eulerian description transforms the governing equations to a fixed reference domain. A high-order discontinuous Galerkin spatial disc...

The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high-order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain is transformed into one on a fixed reference domain by the introduction of a time-dependent mapping that encapsu...

A variety of shooting methods for computing fully discrete time-periodic solutions of partial differential equations, including Newton-Krylov and optimization-based methods, are discussed and used to determine the periodic, compressible, viscous flow around a 2D flapping airfoil. The Newton-Krylov method uses matrix-free GMRES to solve the linear s...

We propose a method to generate high-order unstructured curved meshes using the classical Winslow equations. We start with an initial straight-sided mesh in a reference domain, and fix the position of the nodes on the boundary on the true curved geometry. In the interior of the domain, we solve the Winslow equations using a new continuous Galerkin...

Ahigh-order implicit large-eddy simulation method in two dimensions and three dimensions is used to simulate the aerodynamics of aNACA0012 airfoil over large angles of attack at low chord Reynolds numbers (Re = 5000-50;000). The two-dimensional code is found to have adequate agreement with lift and drag experimental data for prestall angles of atta...

We present a high-order accurate space–time discontinuous Galerkin method for solving two-dimensional compressible flow problems on fully unstructured space–time meshes. The discretization is based on a nodal formulation, with appropriate numerical fluxes for the first and the second-order terms, respectively. The scheme is implicit, and we solve t...

A high-order Implicit Large Eddy Simulations (ILES) method in 2D and 3D is used to simulate a section of a constant spinning straight-bladed vertical-axis wind turbine with two blades at low-Reynolds (Re ≤ 105). The magntiude and frequency content of the blade forces are analyzed and compared to analytical codes and experiments. The maximum power c...

We present a numerical framework for simulation of the compressible Navier-Stokes equations on problems with deforming domains where the boundary motion is prescribed by moving meshes. Our goal is a high-order accurate, efficient, robust, and general purpose simulation tool. To obtain this, we use a discontinuous Galerkin space discretization, diag...

A multiple-fidelity computational framework is presented for designing energetically efficient flapping wings. The goal of this design process is to achieve specific aerodynamics characteristics, namely prescribed lift and thrust coefficients at low energetic cost. The wing kinematics (flapping frequency, flapping amplitude) and the resulting optim...

Many practical applications require the analysis of elastic wave propagation in a homogeneous isotropic media in an unbounded domain. One widely used approach for truncating the infinite domain is the so-called method of perfectly matched layers (PMLs). Most existing PML formulations are developed for finite difference methods based on the first-or...

We present a high-order accurate scheme for coupled fluid–structure interaction problems. The fluid is discretized using a discontinuous Galerkin method on unstructured tetrahedral meshes, and the structure uses a high-order volumetric continuous Galerkin finite element method. Standard radial basis functions are used for the mesh deformation. The...

The simulation of Rotary Friction Welding (RFW) is a challenging task, since it states a coupled problem of phenomena like large plastic deformations, heat flux, contact and friction. In particular the mesh generation and its restoration when using a Lagrangian description of motion is of significant severity. In this regard Implicit Geometry Meshi...

The aeroacoustics of a tuning fork are investigated using a high-order fluid–structure interaction (FSI) scheme. The compressible Navier–Stokes equations are discretized using a discontinuous Galerkin arbitrary Lagrangian–Eulerian (DG-ALE) method on an unstructured tetrahedral mesh, and coupled to a non-linear hyperelastic neo-Hookean model of a tu...

"Low temperature" random matrix theory is the study of random eigenvalues as energy is removed. In standard notation, β is identified with inverse temperature, and low temperatures are achieved through the limit β→∞. In this paper, we derive statistics for low-temperature random matrices at the "soft edge," which describes the extreme eigenvalues f...

We present some recent results for shock capturing using high-order discontinuous Galerkin schemes on fully unstructured meshes. We study the application of sensor-based artificial viscosity to problem with moving shocks, time-stepped using high-order accurate implicit schemes with Jacobian-based Newton-Krylov solvers. We demonstrate that the senso...

We present a high-order accurate scheme for fluid-structure interaction (FSI) simula- tions of flapping flight. The compressible Navier-Stokes equations are discretized using a discontinuous Galerkin arbitrary Lagrangian-Eulerian (DG-ALE) method on an unstruc- tured tetrahedral mesh, and a wing-like structure, represented as a neo-Hookean material,...

We describe a high-order accurate space-time discontinuous Galerkin (DG) method for solving compressible flow problems on two-dimensional moving domains with large deformations. The DG discretization and space-time numerical fluxes are formulated on a three-dimensional space-time domain. The scheme is implicit, and we solve the resulting non-linear...

In this paper a series of two- and three-dimensional, multi-fidelity computational models are presented and used in a preliminary exploration of leading edge vortex (LEV) evolution on pitching and plunging wings. The lower fidelity computational tools (thin airfoil theory and doublet lattice method) are framed in a quasi-inverse design context to d...

In this work, we investigate numerical solvers and time integrators for the system of Ordinary Differential Equations (ODEs) arising from the Discontinuous Galerkin Finite Element Method (DG-FEM) semi-discretization of the Navier-Stokes equations to explore potential speedup opportunities. DG-FEMs have many desirable properties such as sta-bility,...

After several years of planning, the 1st International Workshop on High-Order CFD Methods was successfully held in Nashville, Tennessee, on January 7 and 8, 2012, just before the 50th Aerospace Sciences Meeting. AIAA, AFOSR and DLR provided much needed support, financial and moral. Over 70 participants from all over the world across the research sp...

We present a new line-based discontinuous Galerkin (DG) discretization scheme for first- and second-order systems of partial differential equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements, and it is closely related to the standard nodal DG scheme as well as several of its variants such as the colloc...

The design of efficient flapping wings for human engineered micro aerial vehicles (MAVs) has long been an elusive goal, in part because of the large size of the design space. One strategy for overcoming this difficulty is to use a multifidelity simulation strategy that appropriately balances computation time and accuracy. We compare two models with...

We study some of the properties of a line-based discontinuous Galerkin (DG) scheme for the compressible Euler and Navier-Stokes equations. The scheme is based on fully unstructured meshes of quadrilateral or hexahedral elements, and it is closely related to the standard nodal DG scheme as well as several of its variants such as the collocation-base...

Normal Strombolian activity is possibly one of the most famous examples of cyclic activity in volcanology. The leading paradigm for this type of activity posits that each eruption represents the burst of a large gas slug ascending through liquid magma in the volcanic conduit. When this slug model was first devised, the petrological characteristics...

The present work predicts the formation of laminar separation bubbles at low Reynolds numbers and the related transition to turbulence by means of Implicit Large Eddy Simulations with a high-order Discontinuous Galerkin method. The flow around an SD7003 infinite wing at an angle of attack of 4 degrees is considered at Reynolds numbers of 10 000, 22...

Numerical simulations are becoming increasingly important in the design of micromechanical resonators, in particular for the prediction of complex frequency response in high quality devices. This is particularly true when there is need to accurately predict damping due to anchor losses and other complex wave interactions. Frequency based approaches...

The present work presents a preliminary investigation into the effects of cross-flow on transition at low Reynolds numbers, an area which has essentially remained unexplored. The flow around an in�finite SD7003 wing at an angle of attack of 4�deg is considered at a chord Reynolds numbers of 60,000, and for sweep angles ranging between 0� and 60�deg...

This paper examines some simple uid mechanics principles that may help to understand parachute analysis, performance, and design from a first principles perspective. We start our investigation by applying a basic conservation of momentum and energy analysis to the parachute system. As expected, this analysis illustrates how the wake-velocity defici...