57 citations · 192 across the 23 of their papers we have counts for
24 papers
Direct numerical simulations of the supersonic Taylor--Green vortex via the Boltzmann equation
Tarik Dzanic, Will Trojak, Luigi Martinelli
We explore the dynamics of the three-dimensional compressible Taylor--Green vortex from the perspective of kinetic theory by directly solving the six-dimensional Boltzmann equation…
Second-order invariant-domain preserving approximation to the multi-species Euler equations
Bennett Clayton, Tarik Dzanic, Eric J. Tovar
This work is concerned with constructing a second-order, invariant-domain preserving approximation of the compressible multi-species Euler equations where each species is modeled b…
A method for bounding high-order finite element functions: Applications to mesh validity and bounds-preserving limiters
Tarik Dzanic, Tzanio Kolev, Ketan Mittal
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear boundi…
PyFR v2.0.3: Towards Industrial Adoption of Scale-Resolving Simulations
Freddie D. Witherden, Peter E. Vincent, Will Trojak +17
PyFR is an open-source cross-platform computational fluid dynamics framework based on the high-order Flux Reconstruction approach, specifically designed for undertaking high-accura…
High-order limiting methods using maximum principle bounds derived from the Boltzmann equation I: Euler equations
Tarik Dzanic, Luigi Martinelli
The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In thi…
A note on higher-order and nonlinear limiting approaches for continuously bounds-preserving discontinuous Galerkin methods
Tarik Dzanic
In (Dzanic, J. Comp. Phys., 508:113010, 2024), a limiting approach for high-order discontinuous Galerkin schemes was introduced which allowed for imposing constraints on the soluti…
Continuously bounds-preserving discontinuous Galerkin methods for hyperbolic conservation laws
Tarik Dzanic
For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies…
Direct molecular gas dynamics simulations of re-entry vehicles via the Boltzmann equation
Tarik Dzanic, Luigi Martinelli
This work explores the feasibility of performing three-dimensional molecular gas dynamics simulations of hypersonic flows such as re-entry vehicles through directly solving the six…
DynAMO: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws
Tarik Dzanic, Ketan Mittal, Dohyun Kim +4
We introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost a…
Positivity-preserving discontinuous spectral element methods for compressible multi-species flows
Will Trojak, Tarik Dzanic
We introduce a novel positivity-preserving, parameter-free numerical stabilisation approach for high-order discontinuous spectral element approximations of compressible multi-speci…
Towards full molecular gas dynamics simulations of complex flows via the Boltzmann equation
Tarik Dzanic, Luigi Martinelli
This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substa…
Validation of wall boundary conditions for simulating complex fluid flows via the Boltzmann equation: Momentum transport and skin friction
Tarik Dzanic, Freddie D. Witherden, Luigi Martinelli
The influence and validity of wall boundary conditions for non-equilibrium fluid flows described by the Boltzmann equation remains an open problem. The substantial computational co…
On the anti-aliasing properties of entropy filtering for discontinuous spectral element approximations of under-resolved turbulent flows
Tarik Dzanic, Will Trojak, Freddie D. Witherden
For large Reynolds number flows, it is typically necessary to perform simulations that are under-resolved with respect to the underlying flow physics. For nodal discontinuous spect…
Positivity-preserving entropy filtering for the ideal magnetohydrodynamics equations
Tarik Dzanic, Freddie D. Witherden
In this work, we present a positivity-preserving adaptive filtering approach for discontinuous spectral element approximations of the ideal magnetohydrodynamics equations. This app…
Multi-Agent Reinforcement Learning for Adaptive Mesh Refinement
Jiachen Yang, Ketan Mittal, Tarik Dzanic +5
Adaptive mesh refinement (AMR) is necessary for efficient finite element simulations of complex physical phenomenon, as it allocates limited computational budget based on the need…
A positivity-preserving and conservative high-order flux reconstruction method for the polyatomic Boltzmann--BGK equation
Tarik Dzanic, Freddie D. Witherden, Luigi Martinelli
In this work, we present a positivity-preserving high-order flux reconstruction method for the polyatomic Boltzmann--BGK equation augmented with a discrete velocity model that ensu…
Positivity-Preserving Entropy-Based Adaptive Filtering for Discontinuous Spectral Element Methods
Tarik Dzanic, Freddie D. Witherden
In this work, we present a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. By adapting the filter stren…
Utilizing Time-Reversibility for Shock Capturing in Nonlinear Hyperbolic Conservation Laws
Tarik Dzanic, Will Trojak, Freddie D. Witherden
In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions…
Bounds Preserving Temporal Integration Methods for Hyperbolic Conservation Laws
Tarik Dzanic, Will Trojak, Freddie D. Witherden
In this work, we present a modification of explicit Runge-Kutta temporal integration schemes that guarantees the preservation of any locally-defined quasiconvex set of bounds for t…
Partially-Averaged Navier-Stokes Simulations of Turbulence Within a High-Order Flux Reconstruction Framework
Tarik Dzanic, Sharath Girimaji, Freddie Witherden
High-order methods and hybrid turbulence models have independently shown promise as means of decreasing the computational cost of scale-resolving simulations. The objective of this…
Reinforcement Learning for Adaptive Mesh Refinement
Jiachen Yang, Tarik Dzanic, Brenden Petersen +9
Large-scale finite element simulations of complex physical systems governed by partial differential equations (PDE) crucially depend on adaptive mesh refinement (AMR) to allocate c…
A Riemann Difference Scheme for Shock Capturing in Discontinuous Finite Element Methods
Tarik Dzanic, Will Trojak, Freddie D. Witherden
We present a novel structure-preserving numerical scheme for discontinuous finite element approximations of nonlinear hyperbolic systems. The method can be understood as a generali…
Accuracy, Stability, and Performance Comparison between the Spectral Difference and Flux Reconstruction Schemes
Christopher Cox, Will Trojak, Tarik Dzanic +2
We report the development of a discontinuous spectral element flow solver that includes the implementation of both spectral difference and flux reconstruction formulations. With th…
Fourier Spectrum Discrepancies in Deep Network Generated Images
Tarik Dzanic, Karan Shah, Freddie Witherden
Advancements in deep generative models such as generative adversarial networks and variational autoencoders have resulted in the ability to generate realistic images that are visua…