Zero-RK calculates the thermo-physical properties, reaction rate coefficients, production rates, and other derivatives of the chemically reacting system necessary to efficiently simulate the time evolution of species or thermodynamic state.

Species are the molecules representing the initial reactants, final products, and the stable and unstable intermediates in the reacting system. In a methane burner, for example, the methane fuel (CH4) reacts with oxygen (O2) to form the products water (H2O) and carbon dioxide (CO2). While this process can be modeled by a single global reaction for the four species, greater accuracy is achieved by resolving the intermediate species that are formed during the fuel conversion. This includes stable intermediate species like carbon monoxide (CO), formaldehyde (CH2O) and hydrogen peroxide (H2O2), and highly reactive radical species like atomic hydrogen (H), atomic oxygen (O) and the hydroxyl radical (OH).

Resolving intermediate species is critical to accurately predict the ignition properties and pollutant emissions (e.g., NOx and soot) for commercial combustion applications. However, the use of detailed fuel chemistry for transportation fuels has had limited use in commercial combustor design because of the prohibitive computational cost. Zero-RK directly addresses this challenge and allows design calculations to use more than ten times the number of intermediates.

The highest fidelity models for realistic transportation fuels (e.g., gasoline and diesel) require thousands of intermediate species to be resolved. Zero-RK has been designed to calculate the necessary chemistry quantities in a computationally efficient manner by use of carefully designed algorithms that minimize the number of necessary operations while taking advantage of memory cache and vector arithmetic capabilities present in modern computing processors.


LLNL computational scientists have developed a new technology that solves critical problems for combustion engineers and designers. LLNL’s Zero-Order Reaction Kinetics (Zero-RK) is a software package for simulating chemically reacting systems. Zero-RK’s algorithms dramatically reduce the time to results for many commercial applications, providing in some cases a three-orders-of-magnitude reduction in simulation time. Zero-RK’s feature set, including simulation of zero- and quasi-dimensional reactor systems, reaction sensitivity analyses, and coupling to CFD packages, allows users to simulate a wide variety of systems and devices. These systems include internal combustion engines for automotive and heavy-duty platforms, gas turbines, rocket engines, and industrial burners.


The key innovation inherent in Zero-RK is the sparse, adaptive precondition (SAP) method, which dramatically reduces the cost of integration for chemical systems comprised of many species. In addition, Zero-RK incorporates efficient algorithms for evaluating species’ thermo-physical functions and chemical reaction rates. The resulting improvement in simulation turn-around time is dramatic in many applications. For example, solution time scales linearly with the number of included chemical species in zero-dimensional reactor simulations. For the largest system analyzed, the reduction in simulation time for Zero-RK compared to the best competing commercial package is over ten times. Compared to the best free alternative, Zero-RK achieves a four-thousand-fold reduction in simulation time. These simulation time reductions translate directly to other reactor configurations. Zero-RK has been used to develop a rapid compression machine model that runs in minutes instead of days. When coupled with sophisticated computational fluid dynamics (CFD) packages, Zero-RK based models can reduce the chemistry cost by a factor of seven for realistic transportation fuels.

Prior to Zero-RK, simulations would often take days to complete, even with supercomputers. Due to time restraints and prohibitive computation costs, engineers were forced to use fewer intermediate chemical species, resulting in less accurate simulations and, ultimately, less efficient combustion engines. Zero-RK significantly increased simulation accuracy by allowing calculations to use more than ten times the number of intermediate chemical species for the same computational cost as the best commercial solver while also lowering simulation costs.

Potential Applications

Zero-RK has the ability to perform sensitivity analysis for the development of chemical kinetic methods. Its applications include simulations of fundamental research devices such as shock tubes and rapid compression machines; and commercial applications such as internal combustion engines, gas turbines, rocket engines and industrial burners.

Development Status

Zero-RK has already been used in a variety of combustion applications including engine simulations, research spray vessels, rapid compression machines, mm-scale combustors, and new fuel mechanism development. LLNL has a copyright for Zero-RK.

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